Answer
$x=-\dfrac{7}{2}$ or $x=\dfrac{7}{2}$
Work Step by Step
Dividing both sides by the $GCF=2,$ the given expression, $ 8x^2-98=0 ,$ is equivalent to \begin{align*} \dfrac{8x^2-98}{2}&=\dfrac{0}{2} \\\\ 4x^2-49&=0 .\end{align*} Using the properties of equality, the expression above is equivalent to \begin{align*} 4x^2&=49 \\\\ \dfrac{4x^2}{4}&=\dfrac{49}{4} \\\\ x^2&=\dfrac{49}{4} .\end{align*} Taking the square root of both sides (Square Root Principle), the expression above is equivalent to \begin{align*} x&=\pm\sqrt{\dfrac{49}{4}} \\\\ x&=\pm\dfrac{7}{2} .\end{align*} Hence, the solutions are
$x=-\dfrac{7}{2}$ or $x=\dfrac{7}{2}$.
