Consider $x^{2}-121$. Rewrite $x^{2}-121$ as $x^{2}-11^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.
$$\left(x-11\right)\left(x+11\right)=0$$
To find equation solutions, solve $x-11=0$ and $x+11=0$.
$$x=11$$ $$x=-11$$
Steps by Finding Square Root
Take the square root of both sides of the equation.
$$x=11$$ $$x=-11$$
Steps Using the Quadratic Formula
Subtract $121$ from both sides.
$$x^{2}-121=0$$
This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $1$ for $a$, $0$ for $b$, and $-121$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.
$$x=\frac{0±\sqrt{0^{2}-4\left(-121\right)}}{2}$$
Square $0$.
$$x=\frac{0±\sqrt{-4\left(-121\right)}}{2}$$
Multiply $-4$ times $-121$.
$$x=\frac{0±\sqrt{484}}{2}$$
Take the square root of $484$.
$$x=\frac{0±22}{2}$$
Now solve the equation $x=\frac{0±22}{2}$ when $±$ is plus. Divide $22$ by $2$.
$$x=11$$
Now solve the equation $x=\frac{0±22}{2}$ when $±$ is minus. Divide $-22$ by $2$.
