Answer
$x=\pm\dfrac{7}{3}$
Work Step by Step
Since $x^2=a$ implies $x=\pm\sqrt{a}$ (the Square Root Principle), the solutions to the given equation, $
9x^2-49=0
,$ are
\begin{array}{l}\require{cancel}
9x^2=49
\\\\
x^2=\dfrac{49}{9}
\\\\
x=\pm\sqrt{\dfrac{49}{9}}
\\\\
x=\pm\sqrt{ \left( \dfrac{7}{3} \right)^2}
\\\\
x=\pm\dfrac{7}{3}
.\end{array}
