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.

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

Add 10x to 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.

$$x=1$$