Answer
$\color{blue}{\left\{5, 13\right\}}$
Work Step by Step
Subtract $8$ from each side:
$$(x-9)^2=16$$
Take the square root of both sides:
\begin{align*}
\sqrt{(x-9)^2}&=\pm\sqrt{16}\\
x-9&=\pm4\\
\end{align*}
Add $9$ to both sides:
\begin{align*}
x&=9\pm4\\
x_1&=9-4=5\\
x_2&=9+4=13
\end{align*}
Therefore, the solution set is $\color{blue}{\left\{5, 13\right\}}$.
