#### Answer

$x=\{
-11,9
\}
$

#### Work Step by Step

Since $x^2=a$ implies $x=\pm\sqrt{a}$ (the Square Root Principle), the solutions to the given equation, $
(x+1)^2=100
,$ are
\begin{array}{l}\require{cancel}
x+1=\pm\sqrt{100}
\\\\
x+1=\pm\sqrt{(10)^2}
\\\\
x+1=\pm10
\\\\
x=-1\pm10
.\end{array}
Hence, $
x=\{
-11,9
\}
.$