#### Answer

$x=\left\{ -5-4\sqrt{3},-5+4\sqrt{3} \right\}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
(t+5)^2=48
,$ take the square root of both sides (Square Root Property) and simplify the 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}
t+5=\pm\sqrt{48}
.\end{array}
Simplifying the radical and using the properties of equality to isolate the variable, the equation above is equivalent to
\begin{array}{l}\require{cancel}
t+5=\pm\sqrt{16\cdot3}
\\\\
t+5=\pm\sqrt{(4)^2\cdot3}
\\\\
t+5=\pm4\sqrt{3}
\\\\
t=-5\pm4\sqrt{3}
.\end{array}
The solutions are
\begin{array}{l}\require{cancel}
t=-5-4\sqrt{3}
\\\\\text{OR}\\\\
t=-5+4\sqrt{3}
.\end{array}
Hence, $
x=\left\{ -5-4\sqrt{3},-5+4\sqrt{3} \right\}
.$