Answer
$x=\{-3,13\}$
Work Step by Step
Using $a^2+2ab+b^2=(a+b)^2$ or the factoring of perfect square trinomials, the given equation, $
x^2-10x+25=64
,$ is equivalent to
\begin{array}{l}\require{cancel}
(x-5)^2=64
.\end{array}
Since $x^2=a$ implies $x=\pm\sqrt{a}$ (the Square Root Principle), the solutions to the equation, $
(x-5)^2=64
,$ are
\begin{array}{l}\require{cancel}
x-5=\pm\sqrt{64}
\\\\
x-5=\pm\sqrt{(8)^2}
\\\\
x-5=\pm8
\\\\
x=5\pm8
\\\\
x=\{-3,13\}
.\end{array}