Answer
$\{-7,-1\}$
Work Step by Step
We are given the equation:
$(x+4)^2=9$
Use the Square Root Method (by taking the square root of both sides) to determine the solutions:
$\sqrt{(x+4)^2}=\pm\sqrt 9$
$x+4=\pm 3$
$x+4=-3$ or $x+4=3$
Solve each of the two equations:
\begin{align*}
x+4&=3 &\text{ or}& &x+4=-3\\
x&=3-4 &\text{ or}& &x=-3-4\\
x&=-1 &\text{ or}& &x=-7
\end{align*}
The solution set is:
$\{-7,-1\}$
