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

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

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-2\right)^{2}.

$$x^{2}-4x+4=\left(x+6\right)^{2}$$

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

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

Subtract x^{2} from both sides.

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

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

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

Subtract 12x from both sides.

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

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

$$-16x+4=36$$

Subtract 4 from both sides.

$$-16x=36-4$$

Subtract 4 from 36 to get 32.

$$-16x=32$$

Divide both sides by -16.

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

Divide 32 by -16 to get -2.

$$x=-2$$