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

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

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-3\right)^{2}.

$$x^{2}-6x+9=\left(x+7\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+7\right)^{2}.

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

Subtract x^{2} from both sides.

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

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

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

Subtract 14x from both sides.

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

Combine -6x and -14x to get -20x.

$$-20x+9=49$$

Subtract 9 from both sides.

$$-20x=49-9$$

Subtract 9 from 49 to get 40.

$$-20x=40$$

Divide both sides by -20.

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

Divide 40 by -20 to get -2.

$$x=-2$$