#### Answer

$x=\left\{ 4-\sqrt{3},4+\sqrt{3} \right\}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
(x-4)^2=3
,$ take the square root of both sides (Square Root Property). 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{3}
.\end{array}
Using the properties of equality to isolate the variable, the equation above is equivalent to
\begin{array}{l}\require{cancel}
x=4\pm\sqrt{3}
.\end{array}
The solutions are
\begin{array}{l}\require{cancel}
x=4-\sqrt{3}
\\\\\text{OR}\\\\
x=4+\sqrt{3}
.\end{array}
Hence, $
x=\left\{ 4-\sqrt{3},4+\sqrt{3} \right\}
.$