## Intermediate Algebra: Connecting Concepts through Application

$\color{blue}{\left\{5, 13\right\}}$
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 $\color{blue}{\left\{5, 13\right\}}$.