Consider $x^{2}-64$. Rewrite $x^{2}-64$ as $x^{2}-8^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.
$$\left(x-8\right)\left(x+8\right)=0$$
To find equation solutions, solve $x-8=0$ and $x+8=0$.
$$x=8$$ $$x=-8$$
Steps by Finding Square Root
Add $64$ to both sides. Anything plus zero gives itself.
$$x^{2}=64$$
Take the square root of both sides of the equation.
$$x=8$$ $$x=-8$$
Steps Using the Quadratic Formula
Quadratic equations like this one, with an $x^{2}$ term but no $x$ term, can still be solved using the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$, once they are put in standard form: $ax^{2}+bx+c=0$.
$$x^{2}-64=0$$
This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $1$ for $a$, $0$ for $b$, and $-64$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.
$$x=\frac{0±\sqrt{0^{2}-4\left(-64\right)}}{2}$$
Square $0$.
$$x=\frac{0±\sqrt{-4\left(-64\right)}}{2}$$
Multiply $-4$ times $-64$.
$$x=\frac{0±\sqrt{256}}{2}$$
Take the square root of $256$.
$$x=\frac{0±16}{2}$$
Now solve the equation $x=\frac{0±16}{2}$ when $±$ is plus. Divide $16$ by $2$.
$$x=8$$
Now solve the equation $x=\frac{0±16}{2}$ when $±$ is minus. Divide $-16$ by $2$.
