Completing the square leaving answer in surd form - higher level

This video is all about completing the square and forms part of the higher level playlist of the same name. I've also added to the playlist on GCSE higher revision.

This question is a little difficult as you need to work with fractions. On that basis it's likely that this would be around level 7 - 9, although there's only a few marks available.

Find the values of p and q such that
3xsquared + 5x + 1 = a(x + p)squared + q

Hence, or otherwise, solve and leave your answer in surd form.

It could be done using decimals but this might involve a lot of calculation.

I hope the video helps and please do leave a comment - thanks!

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The course contains around 3 hours of video, quizzes and a copy of my book 'How to get an A in maths.' All the way through to GCSE and just in time for revision.

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[shermaljones]

m8 you are a life saver! i've been staring a question like this for the pass hour now but this video help me solve it. THANK YOU!

[RoseAngella]

Hi. I find it easier (for me) to divide all the terms by 3 and then proceed to Completing the Square. 💚

[turabali]

Only video on YouTube that made me actually understand it

[mahimabegum]

thanks for the help!! my teacher says the take the 3 out of the one as well because 3 is taken out of the whole quadratic but i’m confused because you havent

[rosebudbuddy]

Omd thanks so much mate. I've been full on having a mental breakdown about this for i don't even know how long but you actually are so helpful. Thanks again!

[wediwelday]

Yes!! That was a good question, keep them coming sir 👍

[jessicabam]

Thank you so much 🙏 a total life saver 🙏 regards from South Africa

[san]

Thank you! I was given some exercises to complete and I was confused, even more when I looked at the answers.. however I now completely understand !!

[ollieoldrey]

Thanks very much even though it's 2 years late. In a non-calculator exam that I'm "hopefully" doing next year when I'm doing quadratics with algebraic fractions should I use completing the square if it doesn't factories using the normal split the middle/trial and error method? In a calculator exam, I assume that i should just use the quadratic formula?

[ChristyAdedoyin]

Please this is an urgent question
At the first part why was it -25/36 instead of +25/36

[subarusakamaki]

Hello about the 75/36 since it can be simplified to 25/13. I didn't understand that part why is it 75/36 and not 25/13?

[Roro-lxph]

Thankyou so much sir💓💓You are the best

[tawandabonde]

On the first example why are we dividing by 2 instead of 1/2

[frankisthedaviss]

Hello Simon...
What if we could Factorize The X.?
Just I don't know how it will be ended if we could do that.
Thanks

[priya]

On these types of questions will I be able to use a calculator?

[beckychongo]

What if we had something like this?
12xsquared minuse 6x + 5

[AbbieDenz]

What exam paper is this question from?

[BobBob-uvfq]

Once you (I ) stop mixing up the rules these are actually pretty easy, but just nit getting tripped up

[eipimath]

Thanks for sharing! I posted a video on completing the square using remainder theorem. Let me know what you think.

[charliebrett]

I keep getting 3 (x+5/6)-13/36. EDIT: Don't worry I didn't times the -13/36 by 3.