Answer
$x=\left\{ -8,8 \right\}$
Work Step by Step
Using $a^2-b^2=(a+b)(a-b)$ or the factoring of the difference of two squares, the factored form of the given expression, $
x^2-64=0
,$ is
\begin{array}{l}\require{cancel}
(x-8)(x+8)=0
.\end{array}
Equating each factor to zero (or the Zero-Factor Property), the solutions to the given equation are
\begin{array}{l}\require{cancel}
x-8=0
\\\\
x=8
,\\\\\text{OR}\\\\
x-8=0
\\\\
x=8
.\end{array}
Hence, the solutions are $
x=\left\{ -8,8 \right\}
.$