Answer
$x=\pm\dfrac{\sqrt{35}}{7}$
Work Step by Step
Since $x^2=a$ implies $x=\pm\sqrt{a}$ (the Square Root Principle), the solutions to the given equation, $
7x^2-5=0
,$ are
\begin{array}{l}\require{cancel}
7x^2=5
\\\\
x^2=\dfrac{5}{7}
\\\\
x=\pm\sqrt{\dfrac{5}{7}}
\\\\
x=\pm\sqrt{\dfrac{5}{7}\cdot\dfrac{7}{7}}
\\\\
x=\pm\sqrt{\dfrac{35}{49}}
\\\\
x=\pm\dfrac{\sqrt{35}}{\sqrt{49}}
\\\\
x=\pm\dfrac{\sqrt{35}}{\sqrt{(7)^2}}
\\\\
x=\pm\dfrac{\sqrt{35}}{7}
.\end{array}
