#### Answer

$x=\pm3\sqrt{2}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
4x^2-7=65
,$ use the properties of equality and express the equation in the form $x^2=c.$ 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}
4x^2=65+7
\\\\
4x^2=72
\\\\
x^2=\dfrac{72}{4}
\\\\
x^2=18
.\end{array}
Taking the square root of both sides (Square Root Property), the equation above is equivalent to
\begin{array}{l}\require{cancel}
x=\pm\sqrt{18}
.\end{array}
Writing the radicand as an expression that contains a factor that is a perfect power of the index and then extracting the root of that factor result to
\begin{array}{l}\require{cancel}
x=\pm\sqrt{9\cdot2}
\\\\
x=\pm\sqrt{(3)^2\cdot2}
\\\\
x=\pm3\sqrt{2}
.\end{array}