Answer
$x=\dfrac{2\pm\sqrt{2}}{5}$
Work Step by Step
Taking the square root of both sides, the solutions of the given quadratic equation, $
(5x-2)^2=2
,$ are
\begin{array}{l}\require{cancel}
5x-2=\pm\sqrt{2}
\\\\
5x=2\pm\sqrt{2}
\\\\
x=\dfrac{2\pm\sqrt{2}}{5}
.\end{array}
