Answer
$\left\{-\dfrac{15}{2},\dfrac{5}{2}\right\}$
Work Step by Step
Taking the square root of both sides (Square Root Property), the given equation, $
(2x+5)^2=100
,$ is equivalent to
\begin{align*}
2x+5&=\pm\sqrt{100}
.\end{align*}
Using concepts of simplifying radicals, the equation above is equivalent to
\begin{align*}
2x+5&=\pm\sqrt{(10)^2}
\\
2x+5&=\pm10
.\end{align*}
Using the properties of equality, the equation above is equivalent to
\begin{align*}
2x&=-5\pm10
\\\\
x&=\dfrac{-5\pm10}{2}
\end{align*}\begin{array}{c|c}
x=\dfrac{-5-10}{2} & x=\dfrac{-5+10}{2}
\\\\
x=-\dfrac{15}{2} & x=\dfrac{5}{2}
.\end{array}
Hence, the solution set of $
(2x+5)^2=100
$ is $
\left\{-\dfrac{15}{2},\dfrac{5}{2}\right\}
$.
