Solve (x-3)^2=(x+5)^2

$$( x - 3 ) ^ { 2 } = ( x + 5 ) ^ { 2 }$$

Solve for x

$$x=-1$$

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}.

$$x^{2}-6x+9=\left(x+5\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+5\right)^{2}.

$$x^{2}-6x+9=x^{2}+10x+25$$

Subtract x^{2} from both sides.

$$x^{2}-6x+9-x^{2}=10x+25$$

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

$$-6x+9=10x+25$$

Subtract 10x from both sides.

$$-6x+9-10x=25$$

Combine -6x and -10x to get -16x.

$$-16x+9=25$$

Subtract 9 from both sides.

$$-16x=25-9$$

Subtract 9 from 25 to get 16.

$$-16x=16$$

Divide both sides by -16.

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

Divide 16 by -16 to get -1.

$$x=-1$$