Answer
$\left\{-2,8\right\}$
Work Step by Step
Taking the square root of both sides (Square Root Property), the given equation, $
(x-3)^2=25
,$ is equivalent to
\begin{align*}
x-3&=\pm\sqrt{25}
\\
x-3&=\pm5
.\end{align*}
Using the properties of equality, the equation above is equivalent to
\begin{align*}
x=3\pm5
\end{align*}\begin{array}{l|r}
x=3-5 & x=3+5
\\
x=-2 & x=8
.\end{array}
Hence, the solution set of the equation $
(x-3)^2=25
$ is $\left\{-2,8\right\}$.
