which are steps that could be used to solve 0 = 9(x² + 6x) - 18 by completing the square? check all that…

Explanation:

Step1: Start with the given equation

$0 = 9(x^{2}+6x)-18$ Add 18 to both sides: $18=9(x^{2}+6x)$

Step2: Complete the square inside the parentheses

For the quadratic expression $x^{2}+6x$, to complete the square, we take half of the coefficient of $x$ (half of 6 is 3), and then square it ($3^{2}=9$). We add 9 inside the parentheses on the right - hand side. Since we have a factor of 9 in front of the parentheses, we need to add $9\times9 = 81$ to the left - hand side. So we get $18 + 81=9(x^{2}+6x + 9)$.

Step3: Simplify the right - hand side

The expression $x^{2}+6x + 9=(x + 3)^{2}$, and $18+81 = 99$, so $99=9(x + 3)^{2}$, then $\sqrt{99}=(x + 3)^{2}$ (after taking the square root of both sides in a relevant step of solving).

Answer:

18 + 81 = 9(x^{2}+6x + 9), $\sqrt{99}=(x + 3)^{2}$