#### Answer

$x=\{ -3,7 \}$

#### Work Step by Step

Taking the square root of both sides (the Square Root Property), the solutions to the given equation, $
(x-2)^2=25
,$ are
\begin{array}{l}\require{cancel}
(x-2)=\pm\sqrt{25}
\\\\
x-2=\pm\sqrt{(5)^2}
\\\\
x-2=\pm5
\\\\
x=2\pm5
.\end{array}
Hence, $
x=\{ -3,7 \}
.$