#### Answer

$x=\{-7,13\}$

#### Work Step by Step

Using $a^2+2ab+b^2=(a+b)^2$ or the factoring of perfect square trinomials, the given equation, $
x^2-6x+9=100
,$ is equivalent to
\begin{array}{l}\require{cancel}
(x-3)^2=100
.\end{array}
Since $x^2=a$ implies $x=\pm\sqrt{a}$ (the Square Root Principle), the solutions to the equation, $
(x-3)^2=100
,$ are
\begin{array}{l}\require{cancel}
x-3=\pm\sqrt{100}
\\\\
x-3=\pm\sqrt{(10)^2}
\\\\
x-3=\pm10
\\\\
x=3\pm10
\\\\
x=\{-7,13\}
.\end{array}