Answer
$x=-3$
Work Step by Step
Using the factoring of trinomials in the form $x^2+bx+c,$ the $\text{
equation
}$
\begin{array}{l}\require{cancel}
x^2+6x+9=0
\end{array} has $c=
9
$ and $b=
6
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
3,3
\right\}.$ Using these two numbers, the $\text{
equation
}$ above is equivalent to
\begin{array}{l}\require{cancel}
(x+3)(x+3)=0
\\\\
(x+3)^2=0
.\end{array}
Taking the square root of both sides (Square Root Principle), then
\begin{array}{l}\require{cancel}
x+3=\pm\sqrt{0}
\\\\
x+3=0
\\\\
x=-3
.\end{array}
