#### Answer

$x=\pm5$

#### Work Step by Step

Using the properties of equality, the given equation, $
2x^2+1=51
,$ is equivalent to
\begin{array}{l}\require{cancel}
2x^2=51-1
\\\\
2x^2=50
\\\\
x^2=\dfrac{50}{2}
\\\\
x^2=25
.\end{array}
Taking the square root of both sides, then the solutions of the given equation are
\begin{array}{l}\require{cancel}
x=\pm\sqrt{25}
\\\\
x=\pm\sqrt{(5)^2}
\\\\
x=\pm5
.\end{array}