#### Answer

$x=\left\{ -10,10 \right\}$

#### 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^2-100=0
,$ is
\begin{array}{l}\require{cancel}
(x-10)(x+10)=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-10=0
\\\\
x=10
,\\\\\text{OR}\\\\
x+10=0
\\\\
x=-10
.\end{array}
Hence, the solutions are $
x=\left\{ -10,10 \right\}
.$