Completing the Square - simple method to solve all problems
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- Опубліковано 2 жов 2024
- A simple approach to completing the square, which you can use to solve any type of problem. In the new (2017) syllabus this is a topic at GCSE and IGCSE and is still also a topic at A-level and one of the most useful results from school mathematics.
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Exam in 8 hours! Hopefully I can get 65/70 knowing this! Will comment if I survive :P
Good luck! Yes, let us know how it goes!
@@Mathsaurus Just did the IGCSE Maths paper. It was a weird format and I messed up 1 question as I was panicking. Should get around 62-64/70, but I think the grade boundaries will drop as well. :)
@@watsonmemes8441 Excellent, sounds like it went well then - small mistakes will always happen, so focus on the positive!
@@watsonmemes8441 am i too late to ask how much did u get?😭
@@maryamusman8489 ayyyy ofc not!! i managed to get 8A*s and 1A in French ._. (if i remember correctly ahaha, it's been a little over 2 years). good luck and all the best with your exams! :) i'm surprised i got a notif from a 2 year old comment ahaha, a very pleasant surprise from youtube xd.
i am seeing ur face the first time
Hey I was wondering if you could make a video on arithmetic series for the new IGCSE Edexcel exam. Thank you so much for the help!
Thanks, I'm not sure exactly when I will have time, but yes that's a good idea!
I do not know how to show my boundless appreciation for your videos. All i can do is like and subscribe... Thanks a lot and dont stop making your videos. I am certain I would not score very high without your channel. :)
Thank you, I'm really pleased they have been useful to you and also that you have taken the time to let me know - good luck with your studies!
thanks
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hello sir,you videos have been helping me a lot.I used the above method to solve a problem but the answer is not isn't correct. The expression is 6+4x-x2. Can you tell me how can I complete it using completing squares.
dude i love you, thank you soooo much for helping me out with this amazing method! I can finally submit my boring homework to my teacher xD
Glad I could help!
Hello sir..Can you help me out with this problem.I couldn't solve this complete the square question which is: 2x^2-12x+7 .
I would be your grateful
2(x-3)^2-11
Umm broo... i heard theyre very strict at marking the papers.. and hence i wanna make sure if they wont cut marks if i use this method :D
This method would be acceptable for any maths paper I have seen!
you are a life saver man! keep up the good videos
Hi Kevin, as usual, a fantastic tutorial, thank you. Can I just ask, I assume one will ultimately look to use the completed-square equation to solve for 'x'...e.g. in example 1 ''(x + 2)-squared + 1'') will equal to zero. But when the constant is positive (like in your first example), that will become negative-1 when it is to the RHS...and as that is negative, it can't be square-rooted. Maybe I am mis-understanding something but I understood the purpose of Completing the Square was to put in this format to solve. Appreciate any commentary on this. Thank you.
Yes, everything you say here is correct. Not all quadratics have 2 real roots - some have 1 or none. In the cases where you have to square root a negative as you describe, there are no real roots but....you can find roots that are complex numbers. See this video on the 'discriminant' for some examples and a simple way to work out which case a quadratic fits into ua-cam.com/video/L1XFeD7VZs8/v-deo.html&list=PLUuwecyIK3fjHCs4vf3N0ldO52af-HmwB&index=9. You might also be interested in this video on more general ways of approaching quadratics - ua-cam.com/video/7tU-uUCnALA/v-deo.html .
Thanks Kevin for your reply (I couldn't seem to reply to you directly). So in summary, we should use the Completing the Square (CTS) method when (1) asked to do so, (2) as an alternative to the Quadratic formula when solving the equation / function and (3) when we want the turning points on the function / equation. Would that be correct, please? Would I also be right in saying there is no need to use CTS when we can solve the function with the simple two-brackets method, unless the question specifies we use CTS? Lastly, the functions which yield negative RHS integers (and hence the problem of trying to square-root a negative integer)...is that something you have seen with iGCSE Edexcel questions or is that something more advanced? Many thanks again: your website, video tutorials etc are superb (and as a father who is helping my son with his iGCSE Maths revision, it is most appreciated!).
Yes, generally for solving a quadratic (unless question gives a particular instruction) first try to factorise. This is nice if there's a nice factorisation eg (x-2)(x-3) but if the roots are not nice then use the formula (question will often hint you can't easily factorise by saying that you should give answer to 2dp or similar, ie you'll need to plug something into the calculator). You can prove that the the quadratic formula is just the result of completing the square on quadratics in general, so they are equivalent - so the formula is fine. Completing the square is mathematically direct and nice (and gives a justification for the formula) but most useful in more advanced topics. For example an IGCSE question might say complete the square to give (x+1)^2 +3 and expect the student to identify that this means the minimum is at (-1, 3). I haven't looked at all exam boards but taking negative square roots etc is not in GCSE/IGCSE at all as far as I know. If any of the new syllabuses have included something I'd be very surprised if anything more than just identifying that you can't solve it. But I'm pretty sure not even that - until A-level they generally just avoid these cases.
Is this comment section still alive? If I post a question can I get help?
Can someone solve the question I'm about to post and explain it to me please? Here's the question: y=(x*2)+(7x)-5 can be written in the form y=(x+a)*2+b. Find the value of a and the value of b.
My exam is tommorow
If you just want answers, www.wolframalpha.com will do a lot for you (try just typing in the algebra from your question)
Thank u soooo much for this vid it helped me a lot :)
Great, pleased it was useful!
there is a better way doing this dude
sure there are many methods and ways of writing this sort of problem down. This way has the advantage of making the harder questions (eg where the x^2 coefficient is -3 rather than 1) easier but it might seem strange if you have a method for the easier ones that's something like 'divide the x coefficient by 2 and just sort out the constant', which is a method I also like.
Please sir it's urgent... :(
Keep it up 💯
ur awsome
Thank you!
nice vid
really helpful
abdullah khan acha
@@abdulraffey2733 bacha
First..?
usman mandokhail yea