Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(x-2\right)^{2}$.
$$x^{2}-4x+4+4\left(x-2\right)-32=0$$
Use the distributive property to multiply $4$ by $x-2$.
$$x^{2}-4x+4+4x-8-32=0$$
Combine $-4x$ and $4x$ to get $0$.
$$x^{2}+4-8-32=0$$
Subtract $8$ from $4$ to get $-4$.
$$x^{2}-4-32=0$$
Subtract $32$ from $-4$ to get $-36$.
$$x^{2}-36=0$$
Consider $x^{2}-36$. Rewrite $x^{2}-36$ as $x^{2}-6^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.
$$\left(x-6\right)\left(x+6\right)=0$$
To find equation solutions, solve $x-6=0$ and $x+6=0$.
$$x=6$$ $$x=-6$$
Steps by Finding Square Root
Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(x-2\right)^{2}$.
$$x^{2}-4x+4+4\left(x-2\right)-32=0$$
Use the distributive property to multiply $4$ by $x-2$.
$$x^{2}-4x+4+4x-8-32=0$$
Combine $-4x$ and $4x$ to get $0$.
$$x^{2}+4-8-32=0$$
Subtract $8$ from $4$ to get $-4$.
$$x^{2}-4-32=0$$
Subtract $32$ from $-4$ to get $-36$.
$$x^{2}-36=0$$
Add $36$ to both sides. Anything plus zero gives itself.
$$x^{2}=36$$
Take the square root of both sides of the equation.
$$x=6$$ $$x=-6$$
Steps Using the Quadratic Formula
Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(x-2\right)^{2}$.
$$x^{2}-4x+4+4\left(x-2\right)-32=0$$
Use the distributive property to multiply $4$ by $x-2$.
$$x^{2}-4x+4+4x-8-32=0$$
Combine $-4x$ and $4x$ to get $0$.
$$x^{2}+4-8-32=0$$
Subtract $8$ from $4$ to get $-4$.
$$x^{2}-4-32=0$$
Subtract $32$ from $-4$ to get $-36$.
$$x^{2}-36=0$$
This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $1$ for $a$, $0$ for $b$, and $-36$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.
$$x=\frac{0±\sqrt{0^{2}-4\left(-36\right)}}{2}$$
Square $0$.
$$x=\frac{0±\sqrt{-4\left(-36\right)}}{2}$$
Multiply $-4$ times $-36$.
$$x=\frac{0±\sqrt{144}}{2}$$
Take the square root of $144$.
$$x=\frac{0±12}{2}$$
Now solve the equation $x=\frac{0±12}{2}$ when $±$ is plus. Divide $12$ by $2$.
$$x=6$$
Now solve the equation $x=\frac{0±12}{2}$ when $±$ is minus. Divide $-12$ by $2$.
