Answer
The solution set is $\{-13,5\}$.
Work Step by Step
The given expression is
$\Rightarrow (x+4)^2=81$
$81\geq0$ is a nonnegative number.
Use the square root method.
$\Rightarrow x+4=\pm\sqrt {81}$
Use $\sqrt {81}=9$.
$\Rightarrow x+4=\pm 9$
Subtract $4$ from each side.
$\Rightarrow x+4-4=\pm 9-4$
Simplify.
$\Rightarrow x=\pm 9-4$
The solutions are $x=9-4=5$ and $x=-9-4=-13$
Hence, the solution set is $\{-13,5\}$.
