Answer
$\left\{-\dfrac{8}{7},\dfrac{2}{7}\right\}$
Work Step by Step
Taking the square root of both sides (Square Root Property), the given equation, $
(7x+3)^2=25
,$ is equivalent to
\begin{align*}
7x+3&=\pm\sqrt{25}
.\end{align*}
Using the properties of radicals, the equation above is equivalent to
\begin{align*}\require{cancel}
7x+3&=\pm\sqrt{(5)^2}
\\
7x+3&=\pm5
.\end{align*}
Using the properties of equality, the equation above is equivalent to
\begin{align*}
7x&=-3\pm5
\\\\
x&=\dfrac{-3\pm5}{7}
\end{align*}\begin{array}{l|r}
x=\dfrac{-3-5}{7} & x=\dfrac{-3+5}{7}
\\\\
x=-\dfrac{8}{7} & x=\dfrac{2}{7}
.\end{array}
Hence, the solution set of $
(7x+3)^2=25
$ is $
\left\{-\dfrac{8}{7},\dfrac{2}{7}\right\}
$.
