Answer
The solutions are $x=3$ or $x=-13$.
Work Step by Step
$ x^{2}+10x+25=64\qquad$ ...write left side as a binomial squared.($25=5^{2}$)
$(x+5)^{2}=64\qquad$ ...take square roots of each side.
$ x+5=\pm 8\qquad$ ...add $-5$ to each side.
$ x+5-5=\pm 8-5\qquad$ ...simplify.
$ x=-5\pm 8\qquad$ ...write as separate equations.
$x=-5+8$ or $ x=-5-8\qquad$ ...simplify.
$x=3$ or $x=-13$
