Question

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

Answer 1

Answer:

(x - 4)^2 = 7.

Step-by-step 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

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