Answer
$-7$; $ 7$
Work Step by Step
Given \begin{equation}
-6 m^2+294=0.
\end{equation} Apply the square root property to solve:
\begin{equation}
\begin{aligned}
-6 m^2+294&=0\\
-6 m^2&=-294\\
m^2&=\frac{-294}{-6}\\
m^2&= 49\\
m&= \pm \sqrt{49}\\
m&= \pm 7.
\end{aligned}
\end{equation} Check: \begin{equation}
\begin{aligned}
(-7)^2&\stackrel{?}{=}49\\
49&=49\checkmark\\\\
7^2&\stackrel{?}{=}49\\
49&=49\checkmark.
\end{aligned}
\end{equation} The solution is $m= -7$ or $m= 7$
