Consider $x^{2}-100$. Rewrite $x^{2}-100$ as $x^{2}-10^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.
$$\left(x-10\right)\left(x+10\right)=0$$
To find equation solutions, solve $x-10=0$ and $x+10=0$.
$$x=10$$ $$x=-10$$
Steps by Finding Square Root
Anything plus zero gives itself.
$$x^{2}=100$$
Take the square root of both sides of the equation.
$$x=10$$ $$x=-10$$
Steps Using the Quadratic Formula
Anything plus zero gives itself.
$$x^{2}=100$$
Subtract $100$ from both sides.
$$x^{2}-100=0$$
This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $1$ for $a$, $0$ for $b$, and $-100$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.
$$x=\frac{0±\sqrt{0^{2}-4\left(-100\right)}}{2}$$
Square $0$.
$$x=\frac{0±\sqrt{-4\left(-100\right)}}{2}$$
Multiply $-4$ times $-100$.
$$x=\frac{0±\sqrt{400}}{2}$$
Take the square root of $400$.
$$x=\frac{0±20}{2}$$
Now solve the equation $x=\frac{0±20}{2}$ when $±$ is plus. Divide $20$ by $2$.
$$x=10$$
Now solve the equation $x=\frac{0±20}{2}$ when $±$ is minus. Divide $-20$ by $2$.
