#### Answer

$x=\left\{ -7,3 \right\}
$

#### Work Step by Step

The left side of the given equation, $
x^2+4x+4=25
,$ is a perfect square trinomial whose factored form is
\begin{array}{l}\require{cancel}
(x+2)^2=25
.\end{array}
Taking the square root of both sides (the Square Root Property), the solutions to the given equation are
\begin{array}{l}\require{cancel}
x+2=\pm\sqrt{25}
\\\\
x+2=\pm\sqrt{(5)^2}
\\\\
x=-2\pm5
.\end{array}
Hence, $
x=\left\{ -7,3 \right\}
.$