Answer
$x=\{ -7,3 \}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
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 \}
.$
