weird completing the square when x² > 1

[hot ruin]

the writing in green is the traditional way of completing the square but look at the form they want it in

or this kinda looks like trial and error question

u know first bit of bracket is 2x cos it's $4x^{2}$

[prisma falcon]

bit6411

[hot ruin]

and then u keep putting in numbers for b

and mess around with c ig

worked solution says this which kinda looks like completing the square

[hot ruin]

https://youtu.be/bxZkJYqu6d8 this dude does it in a systematic way

but it's basically a mixture of guessing using ur knowledge of factorisng and completing the square

[harsh drift]

You can get the solution in green into the required form by writing 4 as 2 squared and multiplying the inner bracket by 2

That’s how I would go about it

They don’t often ask you to complete the square in this form tbh, I don’t think this is something to worry about

[winged coral]

so you can actually work out for b

so for this youre right about 2x for 4x^2

but then after that you care about lining up the 12x, because you can use c to fix the constant at the end after

but thinking about (2x + b)^2

expanding that you get

4x^2 + 4bx + b^2

since you want 12x, and you have 4bx

b=3

[hot ruin]

that does not explain how u go from the left expression to the right for last line

[reef umbra]

What exam board?

[hot ruin]

edexcel

[reef umbra]

Is the one in green ur answer

maybe @ another mentor?

[glossy umbra]

multiplied by the denominator

[tall vine]

@hot ruin

[hot ruin]

so there are two ways of approaching this

idk which i prefer

guess it’s good to know both

[olive flower]

Well its easy, since the bracket is equal to 0, just multiple by 2...

[reef umbra]

@hot ruin where is this question from?

[hot ruin]

mock set 6 paper 2H spring 2021

[reef umbra]

oh, so it's a practice paper?

[hot ruin]

in a way. it’s not officially released

[reef umbra]

we're told that practice papers usually contain some sort of error in some way or another

but it's a good question ngl

[hot ruin]

very rarely