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

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

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-5\right)^{2}.

$$x^{2}-10x+25=\left(x+3\right)^{2}$$

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

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

Subtract x^{2} from both sides.

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

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

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

Subtract 6x from both sides.

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

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

$$-16x+25=9$$

Subtract 25 from both sides.

$$-16x=9-25$$

Subtract 25 from 9 to get -16.

$$-16x=-16$$

Divide both sides by -16.

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

Divide -16 by -16 to get 1.

$$x=1$$