Answer
The solutions are $t=-4+3\sqrt{5}$ or $t=-4-3\sqrt{5}$
Work Step by Step
$ t^{2}+8t+16=45\qquad$ ...write left side as a binomial squared. ($16=4^{2}$)
$(t+4)^{2}=45\qquad$ ...take square roots of each side.
$ t+4=\pm\sqrt{45}\qquad$ ...add $-4$ to each side.
$ t+4-4=\pm\sqrt{45}-4\qquad$ ...simplify.
$ t=-4\pm\sqrt{45}\qquad$ ...rewrite $\sqrt{45}$ as $\sqrt{9\cdot 5.}$
$ t=-4\pm\sqrt{9\cdot 5}\qquad$ ...evaluate $\sqrt{9}$.
$ t=-4\pm 3\sqrt{5}\qquad$ ...write as separate equations.
$t=-4+3\sqrt{5}$ or $t=-4-3\sqrt{5}$
