Consider $X^{2}-144$. Rewrite $X^{2}-144$ as $X^{2}-12^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.
$$\left(X-12\right)\left(X+12\right)=0$$
To find equation solutions, solve $X-12=0$ and $X+12=0$.
$$X=12$$ $$X=-12$$
Steps by Finding Square Root
Take the square root of both sides of the equation.
$$X=12$$ $$X=-12$$
Steps Using the Quadratic Formula
Subtract $144$ from both sides.
$$X^{2}-144=0$$
This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $1$ for $a$, $0$ for $b$, and $-144$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.
$$X=\frac{0±\sqrt{0^{2}-4\left(-144\right)}}{2}$$
Square $0$.
$$X=\frac{0±\sqrt{-4\left(-144\right)}}{2}$$
Multiply $-4$ times $-144$.
$$X=\frac{0±\sqrt{576}}{2}$$
Take the square root of $576$.
$$X=\frac{0±24}{2}$$
Now solve the equation $X=\frac{0±24}{2}$ when $±$ is plus. Divide $24$ by $2$.
$$X=12$$
Now solve the equation $X=\frac{0±24}{2}$ when $±$ is minus. Divide $-24$ by $2$.
