Answer
The solutions are $x=-3$ or $x=7$.
Work Step by Step
$g(x)=(x-2)^{2}$
$ g(x)=25\qquad$...substitute $25$ for $g(x)$
$(x-2)^{2}=25$
According to the general principle of square roots:
For any real number $k$ and any algebraic expression $x$ :
$\text{If }x^{2}=k,\text{ then }x=\sqrt{k}\text{ or }x=-\sqrt{k}$.
$ x-2=\pm\sqrt{25}\qquad$...add $2$ to each side.
$ x-2+2=\pm\sqrt{25}+2\qquad$...simplify.
$x=2\pm 5$
$x=2+5$ or $x=2-5$
$x=7$ or $x=-3$
