#### Answer

$x=\{ -4,12 \}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
(x-4)^2=64
,$ take the square root of both sides (Square Root Property) and simplify the resulting radical. Then use the properties of equality to isolate the variable.
$\bf{\text{Solution Details:}}$
Taking the square root of both sides (Square Root Property), the equation above is equivalent to
\begin{array}{l}\require{cancel}
x-4=\pm\sqrt{64}
.\end{array}
Simplifying the radical and using the properties of equality to isolate the variable result to
\begin{array}{l}\require{cancel}
x-4=\pm8
\\\\
x=4\pm8
.\end{array}
The solutions are
\begin{array}{l}\require{cancel}
x=4-8
\\\\
x=-4
\\\\\text{OR}\\\\
x=4+8
\\\\
x=12
.\end{array}
Hence, $
x=\{ -4,12 \}
.$