Consider $m^{2}-36$. Rewrite $m^{2}-36$ as $m^{2}-6^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.
$$\left(m-6\right)\left(m+6\right)=0$$
To find equation solutions, solve $m-6=0$ and $m+6=0$.
$$m=6$$ $$m=-6$$
Steps by Finding Square Root
Subtract $12$ from both sides.
$$m^{2}=48-12$$
Subtract $12$ from $48$ to get $36$.
$$m^{2}=36$$
Take the square root of both sides of the equation.
$$m=6$$ $$m=-6$$
Steps Using the Quadratic Formula
Subtract $48$ from both sides.
$$m^{2}+12-48=0$$
Subtract $48$ from $12$ to get $-36$.
$$m^{2}-36=0$$
This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $1$ for $a$, $0$ for $b$, and $-36$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.
$$m=\frac{0±\sqrt{0^{2}-4\left(-36\right)}}{2}$$
Square $0$.
$$m=\frac{0±\sqrt{-4\left(-36\right)}}{2}$$
Multiply $-4$ times $-36$.
$$m=\frac{0±\sqrt{144}}{2}$$
Take the square root of $144$.
$$m=\frac{0±12}{2}$$
Now solve the equation $m=\frac{0±12}{2}$ when $±$ is plus. Divide $12$ by $2$.
$$m=6$$
Now solve the equation $m=\frac{0±12}{2}$ when $±$ is minus. Divide $-12$ by $2$.
