Solve (x-6)^2=(x+2)^2

$$( x - 6 ) ^ { 2 } = ( x + 2 ) ^ { 2 }$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-6\right)^{2}.

$$x^{2}-12x+36=\left(x+2\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+2\right)^{2}.

$$x^{2}-12x+36=x^{2}+4x+4$$

Subtract x^{2} from both sides.

$$x^{2}-12x+36-x^{2}=4x+4$$

Combine x^{2} and -x^{2} to get 0.

$$-12x+36=4x+4$$

Subtract 4x from both sides.

$$-12x+36-4x=4$$

Combine -12x and -4x to get -16x.

$$-16x+36=4$$

Subtract 36 from both sides.

$$-16x=4-36$$

Subtract 36 from 4 to get -32.

$$-16x=-32$$

Divide both sides by -16.

$$x=\frac{-32}{-16}$$

Divide -32 by -16 to get 2.

$$x=2$$