## Intermediate Algebra: Connecting Concepts through Application

$\color{blue}{\left\{-2, 2\right\}}$
Add $4$ to both sides: $$(p+5)^2=4$$ Take the square root of both sides: \begin{align*} \sqrt{(p+5)^2}&=\pm\sqrt{4}\\ p+5&=\pm2\\ \end{align*} Subtract $5$ from each side: \begin{align*} p&=-5\pm2\\ p_1&=-5-2=-7\\ p_2&=-5+2=-3 \end{align*} Therefore, the solution set is $\color{blue}{\left\{-2, 2\right\}}$.