#### Answer

$x=\left\{ -4,3 \right\}$

#### Work Step by Step

Taking the square root of both sides (the Square Root Property), the solutions to the given equation, $
(2x+1)^2=49
,$ are
\begin{array}{l}\require{cancel}
(2x+1)=\pm\sqrt{49}
\\\\
2x+1=\pm\sqrt{(7)^2}
\\\\
2x+1=\pm7
\\\\
2x=-1\pm7
\\\\
x=\dfrac{-1\pm7}{2}
.\end{array}
Hence, $
x=\left\{ -4,3 \right\}
.$