Answer
$x=\left\{ \dfrac{-5-2\sqrt{3}}{2},\dfrac{-5+2\sqrt{3}}{2} \right\}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
(2x+5)^2=12
,$ take the square root of both sides and simplify the resulting radical. 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}
2x+5=\pm\sqrt{12}
.\end{array}
Extracting the root of the factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
2x+5=\pm\sqrt{4\cdot3}
\\\\
2x+5=\pm\sqrt{(2)^2\cdot3}
\\\\
2x+5=\pm2\sqrt{3}
.\end{array}
Using the properties of equality to isolate the variable results to
\begin{array}{l}\require{cancel}
2x=-5\pm2\sqrt{3}
\\\\
x=\dfrac{-5\pm2\sqrt{3}}{2}
.\end{array}
Hence the solutions are $
x=\left\{ \dfrac{-5-2\sqrt{3}}{2},\dfrac{-5+2\sqrt{3}}{2} \right\}
.$
