## Intermediate Algebra (12th Edition)

$t=\{ -11,-5 \}$
$\bf{\text{Solution Outline:}}$ 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, $t=\{ -11,-5 \} .$