Question

How do you solve `3x^2 – 24x + 24 = 0` using completing the square?

Answer 1

Logical first step: divide everything by `3`

Explanation:

`->x^2-8x+8=0`

Completing the square would mean: taking half of the `x`-coefficient and squaring that:
`x^2-8x+(-4)^2=x^2-8x+16=(x-4)^2`

But we still have to balance the `16` with the `8` we had:
`->x^2-8x+16-8=0`
`->(x-4)^2-8=0->(x-4)^2=8`

So `x-4=sqrt8=2sqrt2->x=4+2sqrt2`
Or `x-4=-sqrt8=-2sqrt2->x=4-2sqrt2`

Often written as `x_(1,2)=4+-2sqrt2`