Answer
$x=\left\{ \dfrac{5-\sqrt{10}}{2},\dfrac{5+\sqrt{10}}{2} \right\}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
(2x-5)^2=10
,$ 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}
2x-5=\pm\sqrt{10}
.\end{array}
Using the properties of equality to isolate the variable, the equation above is equivalent to
\begin{array}{l}\require{cancel}
2x=5\pm\sqrt{10}
\\\\
x=\dfrac{5\pm\sqrt{10}}{2}
.\end{array}
The solutions are
\begin{array}{l}\require{cancel}
x=\dfrac{5-\sqrt{10}}{2}
\\\\\text{OR}\\\\
x=\dfrac{5+\sqrt{10}}{2}
.\end{array}
Hence, $
x=\left\{ \dfrac{5-\sqrt{10}}{2},\dfrac{5+\sqrt{10}}{2} \right\}
.$