Answer
$x=\pm\dfrac{5\sqrt{a}}{3}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To find the solutions of the given equation, $
9x^2-25a=0
,$ isolate first the squared variable. Then take the square root of both sides (Square Root Property) and simplify the resulting radical.
$\bf{\text{Solution Details:}}$
Using the properties of equality, the given equation is equivalent to
\begin{array}{l}\require{cancel}
9x^2=25a
\\\\
x^2=\dfrac{25a}{9}
.\end{array}
Taking the square root of both sides and then simplifying the radical, the equation above is equivalent to
\begin{array}{l}\require{cancel}
x=\pm\sqrt{\dfrac{25a}{9}}
\\\\
x=\pm\sqrt{\dfrac{25}{9}\cdot a}
\\\\
x=\pm\sqrt{\left( \dfrac{5}{3} \right)^2\cdot a}
\\\\
x=\pm\dfrac{5}{3}\sqrt{a}
\\\\
x=\pm\dfrac{5\sqrt{a}}{3}
.\end{array}
