Answer
$\left\{\dfrac{-11\pm\sqrt{7}}{3}\right\}$
Work Step by Step
Taking the square root of both sides (Square Root Property), the given equation, $
(3x+11)^2=7
,$ is equivalent to
\begin{align*}
3x+11&=\pm\sqrt{7}
.\end{align*}
Using the properties of equality, the equation above is equivalent to
\begin{align*}\require{cancel}
3x&=-11\pm\sqrt{7}
\\\\
\dfrac{\cancel3x}{\cancel3}&=\dfrac{-11\pm\sqrt{7}}{3}
\\\\
x&=\dfrac{-11\pm\sqrt{7}}{3}
.\end{align*}
Hence, the solution set of $
(3x+11)^2=7
$ is $
\left\{\dfrac{-11\pm\sqrt{7}}{3}\right\}
$.
