## Intermediate Algebra (12th Edition)

$x=\{ -7,3 \}$
$\bf{\text{Solution Outline:}}$ To solve the given equation, $(x+2)^2=25 ,$ 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} x+2=\pm\sqrt{25} .\end{array} Simplifying the radical and using the properties of equality to isolate the variable result to \begin{array}{l}\require{cancel} x+2=\pm5 \\\\ x=-2\pm5 .\end{array} The solutions are \begin{array}{l}\require{cancel} x=-2-5 \\\\ x=-7 \\\\\text{OR}\\\\ x=-2+5 \\\\ x=3 .\end{array} Hence, $x=\{ -7,3 \} .$