Question

Which are steps that could be used to solve 0 = 9(x2 + 6x) – 18 by completing the square? Check all that apply.

18 + 81 = 9(x2 + 6x + 9)

18 + 9 = 9(x2 + 6x + 9)

18 + 36 = 9(x2 + 6x + 36)

11 = (x + 3)2


= (x + 6)2


= (x + 3)2

Answer 1

Explanation:

Answer 2

18 + 81 = 9(x² + 6x + 9)
11 = (x + 3)²

When we are completing the square, we are going to move the value of c across the equals. We will do that by adding, and end up with

18=9(x²+6x)

We take the value of b (the coefficient of x), divide it by 2 and square it:
(6/2)²=3²=9

This is the value that completes the square. However, since the entire square is multiplied by 9, this value must be multiplied by 9 before we can add it across the equals:
18+9(9) = 9(x²+6x+9)
18+81=9(x²+6x+9)
99=9(x²+6x+9)

Dividing both sides by 9, we have:
11=x²+6x+9

11=(x+3)²