#### Answer

$t=-5\pm2\sqrt{3}$

#### Work Step by Step

Since $x^2=a$ implies $x=\pm\sqrt{a}$ (the Square Root Principle), the solutions to the given equation, $
(t+5)^2=12
,$ are
\begin{array}{l}\require{cancel}
t+5=\pm\sqrt{12}
\\\\
t+5=\pm\sqrt{4\cdot3}
\\\\
t+5=\pm\sqrt{(2)^2\cdot3}
\\\\
t+5=\pm2\sqrt{3}
\\\\
t=-5\pm2\sqrt{3}
.\end{array}