Solve (x+7)^2=(x-3)^2

$$( x + 7 ) ^ { 2 } = ( x - 3 ) ^ { 2 }$$

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+7\right)^{2}.

$$x^{2}+14x+49=\left(x-3\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.

$$x^{2}+14x+49=x^{2}-6x+9$$

Subtract x^{2} from both sides.

$$x^{2}+14x+49-x^{2}=-6x+9$$

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

$$14x+49=-6x+9$$

Add 6x to both sides.

$$14x+49+6x=9$$

Combine 14x and 6x to get 20x.

$$20x+49=9$$

Subtract 49 from both sides.

$$20x=9-49$$

Subtract 49 from 9 to get -40.

$$20x=-40$$

Divide both sides by 20.

$$x=\frac{-40}{20}$$

Divide -40 by 20 to get -2.

$$x=-2$$