Consider $x^{2}-81$. Rewrite $x^{2}-81$ as $x^{2}-9^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.
$$\left(x-9\right)\left(x+9\right)=0$$
To find equation solutions, solve $x-9=0$ and $x+9=0$.
$$x=9$$ $$x=-9$$
Steps by Finding Square Root
Take the square root of both sides of the equation.
$$x=9$$ $$x=-9$$
Steps Using the Quadratic Formula
Subtract $81$ from both sides.
$$x^{2}-81=0$$
This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $1$ for $a$, $0$ for $b$, and $-81$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.
$$x=\frac{0±\sqrt{0^{2}-4\left(-81\right)}}{2}$$
Square $0$.
$$x=\frac{0±\sqrt{-4\left(-81\right)}}{2}$$
Multiply $-4$ times $-81$.
$$x=\frac{0±\sqrt{324}}{2}$$
Take the square root of $324$.
$$x=\frac{0±18}{2}$$
Now solve the equation $x=\frac{0±18}{2}$ when $±$ is plus. Divide $18$ by $2$.
$$x=9$$
Now solve the equation $x=\frac{0±18}{2}$ when $±$ is minus. Divide $-18$ by $2$.
