I'm a 70-year-old woman & I'm enjoying your refresher course. I'm finding that I don't remember the names of the equations, but they are still relevant & I can recall them, so this is actually fun!
I must admit, being pretty cranky at maths but at the same time finding it interesting, I do appreciate this guy's cautious approach. Definitely gave it a like.
I mean this constructively: Really wish that you got to the point faster and were just more concise overall. It's hard to click on your videos because of how they drag on.
@My Reading Room Channel I wouldn't call it spreading nonsense, but he really just ought to get to the point and stick to it. But it's his channel, he'll do what makes him happy.
Some ppl love the sound of their own voices. That said, when ppl used to seek my help/advice as a senior military leader, I'd tell them, "the price of admission is that you have to put up with who I am." This of course didn't apply in emergency circumstances where I hope I always got to the damn point before people died.
@@Sardit I have already told UA-cam to not recommend this channel. It's not worth my time. Sad, because he is a knowledgeable and passionate guy. Just a bad presenter.
The quadratic equation always works of course but since the quadratic equation is really derived from "completing the square" which is the geometric interpretation of the algebraic approach, I usually complete the square when factoring isn't immediately obvious. To complete the square, rewrite the quadratic equation placing the constant on the right side of the equal symbol. Next rewrite the equation thusly: (x + b/2)^2 = c + (b/2)^2. Simplify and take the square root of both sides and solve for x, (you will get 2 answers)
@@ainsworth501 yes, I mean the quadratic formula, which is not the same thing as a quadratic equation. The proofreader was on vacation when I posted this!
Learned all this, along with many other disciplines. The only ones I actually used in life? Arithmetic and English. That's it. Yes, I know, students headed for engineering, science etc. WILL have used these. I would wager the vast majority never did? Had it been an option, I would have binned everything, save for Arithmetic and English, and taken apprenticeships in skills that guaranteed work early on.
I never learnt all this. I went through maths classes, understood nothing, had very bad (appallingly bad) grades. Private tuition taught me little procedures I applied blindly, without thinking. Since I left secondary school, i've avoided maths. Partly because of courses like this: I have no idea what all of it is about.And yes, I have watched it. But it's intended for people who can actually understand. Nothing wrong with that.
@@zerobeat2020 His channel is geared to high school student/college students. I sort of meant the comment as joke; too many students fail to realize that another part of the brain must be engaged to study math, the sciences then is engaged to study history or social science. We read a history book and get the general idea, while study of science/math requires something more active from the brain. Anything that helps the student to understand math is to the good.
I love your channel. I learned a lot from it. I am high school class of 83, so I don't think we are that much apart age wise since that you mentioned the 80' a lot. Brother, if you want my honest opinion, you talk too much. You want to get to the point, because I want to watch more of your videos.
I’m with you! He should STFU and just solve the damn problem. If I were in his class, I would daydream about doing unspeakable things. Just skip ahead to about the 6 minute mark, if you want to see how he solves a problem.
@@glasshalffull8625 I dont have a particular draw for math. Having said that, this guy works for me. No nonsense just teachs: ua-cam.com/video/MJyslbVZ5sI/v-deo.html
I appreciate your empathetic explanation to fundamental terminologies, 🧮 as for the familiarisation of set, or evolving formulas, that would be my next pursuit, Teach . Be Well 🍎🙏🙂
with this one it was get to one side x - x - 1 = 0 see if it factors easily .... then had to remember the quadratic equation x = [-b (+/-)square-root (b^2 - 4ac)]/2a
You've already told us in a previous video that √9 = ±3 so _according to you_ the two solutions are x = (1+√5)/2. _According to you_ this is two distinct real numbers. If what you said about √9 was true - which it isn't, of course - you would need to write x = (1+|√5|)/2 and (1-|√5|)/2 to distinguish between the two roots.
@@robertakerman3570 Not if you listen to this guy. He is the worst "teacher" I have ever come across. He will only confuse and disillusion you further.
“The Six Million Dollar Man” starring Lee Majors as Steve Austin. Lindsay Wagner was “The Bionic Woman,” a spin-off. Sorry for the aside. Back to math. ;-)
JUST SAY NO! to memorizing the quadratic formula! Use "forced factorization": an intuitive algebraic approach to solving quadratics that works whether or not clean/rational factors exist (without memorizing any formulas). Simply force x^2+bx+c into factored form (x+r)(x+s) and find factors r and s (and the zeros will just be -r and -s). How to find r and s? From binomial multiplication of (x+r)*(x+s), we know r and s add to b and r and s multiply to c. So we get two equations: r+s=b and r*s=c. The trick to solving these 2 equations (without stumbling right back into the original quadratic) is to rewrite them in terms of the m="midpoint of r and s" and d= "distance from midpoint to r and s". The midpoint of any two numbers is just their sum over 2, so m=(r+s)/2. But from the first equation, r+s=c, so m =(r+s)/2=c/2. Because m is the midpoint of r and s, it's the same distance "d" from both r and s. So r=(m-d)=(c/2-d) and s=(m+d)=(c/2+d). Now a cool thing now happens when plug these m&d versions of r and s into the second equation r*s=b. The product of r*s becomes (m-d)*(m+d)=m^2-d^2. After calculating m=c/2, it is trivial to solve for d. We then plug m and d back into equations for r and s, and the zeros of x=-r and x=-s fall right out. This sounds cumbersome, but just watch the ease of using it, no memorization needed: Applied to x^2-x-1=0, we get: r*s=-1 and r+s=-1. Since c=-1, we have m= c/2 = -1/2. Thus r=(-1/2-d) and s=(-1/2+d). Thus r*s =-1 = (-1/2-d)*(-1/2+d)=1/4-d^2. Solving 1/4-d^2=-1 with algebra gives d=sqrt(5/4). Thus r=(m-d)=(-1/2-sqrt(5/4)) and s=(m+d)=(-1/2+d=-1/2+sqrt(5/4)). The zeros of x are just {-r,-s}, which simplifies to {1/2+sqrt(5/4), 1/2-sqrt(5/4)}.
The problem with his answer I have is that it is incomplete math. If x1 and x2 are both correct answers then you should be able to finish the math and get 1 when you plug it in. (1+sqr(5))÷2 gets the answer of 1, but when you switch it to subtracting the sqr(5) you can't plug it in the same. So the true answer is (1+sqr(5))÷2.
I would argue that if the discriminate equals zero then the quadratic equation has only 1 solution. The vertex of the parabola will touch the x axis, but the parabola itself does not cross over it.
I copied down everything my math instructor wrote on the board, reread it again and again, only to get a mark of 52%, where passing grade was 60. Obviously, the instructor’s notation wasn’t “notes”. I’ve felt cheated ever since. Fortunately 99% of all this mystery was irrelevant to my career.
When the parabola is tangent to the x-axis, there is only one solution....also if it doesn't cross the x-axis there will be two imaginary or complex solutions that are not real....
9:50 two binomials?... I think that's a contamination sir. It's either a binomial or 2 factors, isn't it? 2 binomials would be 2 two-part expressions. 😜
You said that completing the square is the 'long version of the quadratic formula'? Can you really mean or even justify that? I cannot believe an experienced maths teacher could ever say that? In using the CTS method you don't even have to have the equation equal to zero and can start from the problem as given, you can easily do it in four, perhaps five lines of working. How can it be a longer version of the quadratic formula. I agree it is harder for students to learn, and in my experience they don't like CTS or can even do correctly most of the time and the formula is a safer bet but once mastered it is far easier all round, perhaps even easier than factoring. Are you confusing that CTS on the ax^2 +bx + c =0 ( a, b, c unknown) which is how the formula is obtained but with a, b, c known it is much easier once you learn the quick method of CTS. Again an experienced math teacher one would know this. Also you state that a quadratic always has two roots or answers, and while 'true' it's going to confuse students when they get an equation like x^2 -2x +1 = 0 and find they have only value of x (in this case x=1), as an experienced teacher to prevent any such confusion one should really have mentioned that you can have a repeated root, so in this example x =1 and x=1.
Blah blah blah. You would make a 8 min video for X+2 = 4. You actually do a disservice to math education. Concision and clarity are part of the beauty of mathematics - quit yapping and do the math without so much BS.
I am not a fan of this is the best 👍 and a half years ago and I have to say I am a big fan of the world 🌏 and a few others are doing it for the money and the other one of the first and the rest of the day before I
Probably the worst mathematics channel I've come across because you waste so much time. Just get to the point. As much as you want to break things down you just end up making things more confusing 🤦♂️
OIR BIEN TEACHER ESTOS VIDEOS SON UN NERVES ACTIVATE FOR FEW MALE AND FEMALES , PARECE QUE EN ESTE TIEMPO HAY UN GRUPO DE GRUPIS QUE NO SE CONOCEN PERO YO SE COMO IDENTIFICARLOS , SOLO BUSCAN EQUATIONS , ALL WHAT YOU GIVE …I DO NOT KNOW WHAT WILL HAPPEN PERO YO SE QUE ALGO BELLO SE INICIARA , YO ESPERO , YO HABLO LAS DOS LENGUAS …VOY A SER HAPPY!!!😀😃😄😁😆🥲🤣😂😅
I'm a 70-year-old woman & I'm enjoying your refresher course. I'm finding that I don't remember the names of the equations, but they are still relevant & I can recall them, so this is actually fun!
I must admit, being pretty cranky at maths but at the same time finding it interesting, I do appreciate this guy's cautious approach. Definitely gave it a like.
I mean this constructively: Really wish that you got to the point faster and were just more concise overall. It's hard to click on your videos because of how they drag on.
@My Reading Room Channel I wouldn't call it spreading nonsense, but he really just ought to get to the point and stick to it. But it's his channel, he'll do what makes him happy.
Some ppl love the sound of their own voices. That said, when ppl used to seek my help/advice as a senior military leader, I'd tell them, "the price of admission is that you have to put up with who I am." This of course didn't apply in emergency circumstances where I hope I always got to the damn point before people died.
I hate to agree, but I have to… and I need to stop his videos from being recommended.
@@Sardit I have already told UA-cam to not recommend this channel. It's not worth my time. Sad, because he is a knowledgeable and passionate guy. Just a bad presenter.
Damn - y'all are rude. This is an outstanding teacher!
The quadratic equation always works of course but since the quadratic equation is really derived from "completing the square" which is the geometric interpretation of the algebraic approach, I usually complete the square when factoring isn't immediately obvious. To complete the square, rewrite the quadratic equation placing the constant on the right side of the equal symbol. Next rewrite the equation thusly: (x + b/2)^2 = c + (b/2)^2. Simplify and take the square root of both sides and solve for x, (you will get 2 answers)
Do you mean the quadratic formula?
@@ainsworth501 yes, I mean the quadratic formula, which is not the same thing as a quadratic equation. The proofreader was on vacation when I posted this!
Learned all this, along with many other disciplines. The only ones I actually used in life? Arithmetic and English. That's it.
Yes, I know, students headed for engineering, science etc. WILL have used these. I would wager the vast majority never did?
Had it been an option, I would have binned everything, save for Arithmetic and English, and taken apprenticeships in skills that guaranteed work early on.
I never learnt all this. I went through maths classes, understood nothing, had very bad (appallingly bad) grades. Private tuition taught me little procedures I applied blindly, without thinking.
Since I left secondary school, i've avoided maths.
Partly because of courses like this: I have no idea what all of it is about.And yes, I have watched it.
But it's intended for people who can actually understand. Nothing wrong with that.
Lesson starts at 8:04
It takes 16 minutes to solve that? 1 minute to solve; 15 minutes preaching...
My mind would just say: (X) x (X) = 2X minus... I'm hopeless.
@@robertakerman3570 noo, two times x is 2x, x^2 is X times X not 2 times x
@@CreepDestroyer True but it's difficult 4 Me to remember so many things. It IS fun 2 watch though.
I am also puzzled Steven. I thought this would be an interesting channel, but I guess this is not aimed at us.
@@zerobeat2020 His channel is geared to high school student/college students. I sort of meant the comment as joke; too many students fail to realize that another part of the brain must be engaged to study math, the sciences then is engaged to study history or social science. We read a history book and get the general idea, while study of science/math requires something more active from the brain.
Anything that helps the student to understand math is to the good.
I love your channel. I learned a lot from it. I am high school class of 83, so I don't think we are that much apart age wise since that you mentioned the 80' a lot. Brother, if you want my honest opinion, you talk too much. You want to get to the point, because I want to watch more of your videos.
I left school in 1965 and worked in construction planning for many years and I never used algebra.
OMG, if all your courses end up being the rhetorical run around this one turned out to be, you can count me out of your course series.
I’m with you! He should STFU and just solve the damn problem. If I were in his class, I would daydream about doing unspeakable things. Just skip ahead to about the 6 minute mark, if you want to see how he solves a problem.
@@glasshalffull8625 Nah, the better solution is to skip this guy altogether.
@@harrymallory7963 I know I should, but mathematics has a strong draw for me. Can you recommend a better math UA-camr?
@@glasshalffull8625 I dont have a particular draw for math. Having said that, this guy works for me. No nonsense just teachs:
ua-cam.com/video/MJyslbVZ5sI/v-deo.html
I appreciate your empathetic explanation to fundamental terminologies, 🧮 as for the familiarisation of set, or evolving formulas, that would be my next pursuit, Teach .
Be Well 🍎🙏🙂
The great mathematics teacher
with this one it was get to one side x - x - 1 = 0 see if it factors easily .... then had to remember the quadratic equation x = [-b (+/-)square-root (b^2 - 4ac)]/2a
You've already told us in a previous video that √9 = ±3 so _according to you_ the two solutions are
x = (1+√5)/2. _According to you_ this is two distinct real numbers. If what you said about √9 was true - which it isn't, of course - you would need to write x = (1+|√5|)/2 and (1-|√5|)/2 to distinguish between the two roots.
As if I'm not confused enuf-someday it will sink in
@@robertakerman3570 Not if you listen to this guy. He is the worst "teacher" I have ever come across. He will only confuse and disillusion you further.
@@PureExile Maybe He teaches "baby-talk" as a go/to foundation, only to have students relearn as they develop. I dunno.
@@robertakerman3570 Check out his "A train went 30 miles in 17 minutes..." video. It is actually hilarious!
@@PureExile Might have seen it, I'm watching R.Beato now
“The Six Million Dollar Man” starring Lee Majors as Steve Austin. Lindsay Wagner was “The Bionic Woman,” a spin-off. Sorry for the aside. Back to math. ;-)
JUST SAY NO! to memorizing the quadratic formula!
Use "forced factorization": an intuitive algebraic approach to solving quadratics that works whether or not clean/rational factors exist (without memorizing any formulas). Simply force x^2+bx+c into factored form (x+r)(x+s) and find factors r and s (and the zeros will just be -r and -s). How to find r and s?
From binomial multiplication of (x+r)*(x+s), we know r and s add to b and r and s multiply to c. So we get two equations: r+s=b and r*s=c. The trick to solving these 2 equations (without stumbling right back into the original quadratic) is to rewrite them in terms of the m="midpoint of r and s" and d= "distance from midpoint to r and s". The midpoint of any two numbers is just their sum over 2, so m=(r+s)/2. But from the first equation, r+s=c, so m =(r+s)/2=c/2. Because m is the midpoint of r and s, it's the same distance "d" from both r and s. So r=(m-d)=(c/2-d) and s=(m+d)=(c/2+d). Now a cool thing now happens when plug these m&d versions of r and s into the second equation r*s=b. The product of r*s becomes (m-d)*(m+d)=m^2-d^2. After calculating m=c/2, it is trivial to solve for d. We then plug m and d back into equations for r and s, and the zeros of x=-r and x=-s fall right out. This sounds cumbersome, but just watch the ease of using it, no memorization needed:
Applied to x^2-x-1=0, we get: r*s=-1 and r+s=-1. Since c=-1, we have m= c/2 = -1/2. Thus r=(-1/2-d) and s=(-1/2+d). Thus r*s =-1 = (-1/2-d)*(-1/2+d)=1/4-d^2. Solving 1/4-d^2=-1 with algebra gives d=sqrt(5/4). Thus r=(m-d)=(-1/2-sqrt(5/4)) and s=(m+d)=(-1/2+d=-1/2+sqrt(5/4)). The zeros of x are just {-r,-s}, which simplifies to {1/2+sqrt(5/4), 1/2-sqrt(5/4)}.
Thank you!
SET THE EQUATION EQUAL TO ZERO by adding 1 to each side of this equation.
subtract 1 from both sides
The problem with his answer I have is that it is incomplete math. If x1 and x2 are both correct answers then you should be able to finish the math and get 1 when you plug it in. (1+sqr(5))÷2 gets the answer of 1, but when you switch it to subtracting the sqr(5) you can't plug it in the same. So the true answer is (1+sqr(5))÷2.
This GenXer remembers the quality of his ‘notes’ during math class back in the day too
You are excellent
thank you.
I would argue that if the discriminate equals zero then the quadratic equation has only 1 solution. The vertex of the parabola will touch the x axis, but the parabola itself does not cross over it.
Subtract 1 from both sides, then use the Quadratic Formula.
Yes I'm am there's all subject as well
I copied down everything my math instructor wrote on the board, reread it again and again, only to get a mark of 52%, where passing grade was 60. Obviously, the instructor’s notation wasn’t “notes”. I’ve felt cheated ever since. Fortunately 99% of all this mystery was irrelevant to my career.
Lots of self promotion filler.
When the parabola is tangent to the x-axis, there is only one solution....also if it doesn't cross the x-axis there will be two imaginary or complex solutions that are not real....
Way too slow to get into the answer,3 mins in and it’s a quadratic,irritating
9:50 two binomials?... I think that's a contamination sir. It's either a binomial or 2 factors, isn't it? 2 binomials would be 2 two-part expressions. 😜
The ozone layer
First step? A 12 min nap.
What's the first step ?
Get an equation that equals zero.
x squared - x = 1 x squared - x - 1 = 0
MAN! HOW MUCH COFFEE DO YOU CONSUME!!!!!!!!??????? WHEW!!
Yay, Steve Austin - the Binomial Man. We can rebuild him!
Nothing, we let you figure it out.
You said that completing the square is the 'long version of the quadratic formula'? Can you really mean or even justify that? I cannot believe an experienced maths teacher could ever say that? In using the CTS method you don't even have to have the equation equal to zero and can start from the problem as given, you can easily do it in four, perhaps five lines of working. How can it be a longer version of the quadratic formula. I agree it is harder for students to learn, and in my experience they don't like CTS or can even do correctly most of the time and the formula is a safer bet but once mastered it is far easier all round, perhaps even easier than factoring. Are you confusing that CTS on the ax^2 +bx + c =0 ( a, b, c unknown) which is how the formula is obtained but with a, b, c known it is much easier once you learn the quick method of CTS. Again an experienced math teacher one would know this. Also you state that a quadratic always has two roots or answers, and while 'true' it's going to confuse students when they get an equation like x^2 -2x +1 = 0 and find they have only value of x (in this case x=1), as an experienced teacher to prevent any such confusion one should really have mentioned that you can have a repeated root, so in this example x =1 and x=1.
I'm impressed that "everyone" knows the solution, yet continue to tune in. I'm jus' tryin to learn.
@@robertakerman3570 not sure what you mean. I'm not offering any solutions just referring to some statements that I think are incorrect.
@@markjakeway2035 You said it well. I'm just saying if I knew as much as U, I'd B working for JPL(Haha). UR 2 smart 4 this stuff.
I just fenagled the equation and got X=-1
x^2-x=1
x(x-1)=1
x=1/(x-1) mult both sid by x
2x=x/x(x-1)
2x=x-1
x=-1 🤔
I know I broke some form of algebraic law here but idk what it was. I just like how simple it was!
Multiply both sides by x gives x squared on the left not 2x
2 errors in line 4 for starters... Mult both sides by x gives x^2 = x^2/(x-1). You're going round in circles then!
Much of the video is off-topic.
I think you mean the 6million dollar man
phi
......nice.
Jhon❤👌🏿📚👌🏿
Yes and yes I am not good money's and my disability
What you do first is , rub it out that solves it !.
YOU TALK TOO MUCH!!!! Get on with the example.
Blah blah blah. You would make a 8 min video for X+2 = 4. You actually do a disservice to math education. Concision and clarity are part of the beauty of mathematics - quit yapping and do the math without so much BS.
Teacher. Your buying time not personality.
I don't even want to know. Algebra is useless 😁
I am not a fan of this is the best 👍 and a half years ago and I have to say I am a big fan of the world 🌏 and a few others are doing it for the money and the other one of the first and the rest of the day before I
Probably the worst mathematics channel I've come across because you waste so much time. Just get to the point. As much as you want to break things down you just end up making things more confusing 🤦♂️
🎉🎉🎉🎉🎉🎉🎉🎉🎉❤❤❤❤❤❤❤❤❤❤❤❤😂😂😂😂😂😂😂😂😊😊😊😊😊😊😊😊😊😊😊
Po Len Sho
Like the videos…but jeeez….16 min to solve a simple problem. Please get to the point of solving without so much BS.
Too much talking for his simple task
7 minutes to get to the point….. are you for real?
5:12 of blah, blah, blah, including a self serving ad, then lots more blah, blah…
the endless bullshit is too much to sit through. see ya.
Go to the point. You talk too much.
Answer: Grab the eraser and erase the "problem" from the board.... taadaa "problem" solved!!
Love you, but maybe lay off the coffee.
The first and only thing you do is "click" out of this boring shit!
OIR BIEN TEACHER ESTOS VIDEOS SON UN NERVES ACTIVATE FOR FEW MALE AND FEMALES , PARECE QUE EN ESTE TIEMPO HAY UN GRUPO DE GRUPIS QUE NO SE CONOCEN PERO YO SE COMO IDENTIFICARLOS , SOLO BUSCAN EQUATIONS , ALL WHAT YOU GIVE …I DO NOT KNOW WHAT WILL HAPPEN PERO YO SE QUE ALGO BELLO SE INICIARA , YO ESPERO , YO HABLO LAS DOS LENGUAS …VOY A SER HAPPY!!!😀😃😄😁😆🥲🤣😂😅
Subtract 1 from both sides