Answer
$x=\left\{ -3-\sqrt{11},-3+\sqrt{11} \right\}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
(x+3)^2=11
,$ take the square root of both sides (Square Root Property). 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+3=\pm\sqrt{11}
.\end{array}
Using the properties of equality to isolate the variable, the equation above is equivalent to
\begin{array}{l}\require{cancel}
x=-3\pm\sqrt{11}
.\end{array}
The solutions are
\begin{array}{l}\require{cancel}
x=-3-\sqrt{11}
\\\\\text{OR}\\\\
x=-3+\sqrt{11}
.\end{array}
Hence, $
x=\left\{ -3-\sqrt{11},-3+\sqrt{11} \right\}
.$
