#### Answer

$x=\pm3\sqrt{3}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
2x^2+7=61
,$ 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}
2x^2=61-7
\\\\
2x^2=54
\\\\
x^2=\dfrac{54}{2}
\\\\
x^2=27
.\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{27}
.\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\cdot3}
\\\\
x=\pm\sqrt{(3)^2\cdot3}
\\\\
x=\pm3\sqrt{3}
.\end{array}