#### Answer

$t=\{ -11,-5 \}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
(t+8)^2=9
,$ 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}
t+8=\pm\sqrt{9}
.\end{array}
Simplifying the radical and using the properties of equality to isolate the variable result to
\begin{array}{l}\require{cancel}
t+8=\pm3
\\\\
t=-8\pm3
.\end{array}
The solutions are
\begin{array}{l}\require{cancel}
t=-8-3
\\\\
t=-11
\\\\\text{OR}\\\\
t=-8+3
\\\\
t=-5
.\end{array}
Hence, $
t=\{ -11,-5 \}
.$