Question

-3x^2 plus 24x = 27
complete the square

Answer 1

(x - 4)^2 = 7.

Explanation:

-3x^2 + 24x = 27

-3(x^2 - 8x) = 27 Divide through by -3:

(x^2 - 8x) = -9 Divide the -8 by 2. Now (x - 4)^2 = x^2 - 8x + 16 so:

(x - 4)^2 - 16 = -9

(x - 4)^2 = 16 - 9

(x - 4)^2 = 7.

Answer 2

You can divide the whole expression by -3:

`-3x^2+24x=27 \iff x^2-8x = -9`

Recalling that

`(x-a)^2=x^2-2ax+a^2`

Let's compare the middle term:

`-8x = -2ax \iff a=4`

So, we want to complete

`(x-4)^2 = x^2-8x+16`

Which differs from
`x^2-8x` by 16. So, if we add 16 to both sides, we have

`x^2-8x=-9 \iff x^2-8x+16=7 \iff (x-4)^2=7`