Solve (x+1)^2=(3-x)^2

$$( x + 1 ) ^ { 2 } = ( 3 - x ) ^ { 2 }$$

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+1\right)^{2}.

$$x^{2}+2x+1=\left(3-x\right)^{2}$$

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

$$x^{2}+2x+1=9-6x+x^{2}$$

Add 6x to both sides.

$$x^{2}+2x+1+6x=9+x^{2}$$

Combine 2x and 6x to get 8x.

$$x^{2}+8x+1=9+x^{2}$$

Subtract x^{2} from both sides.

$$x^{2}+8x+1-x^{2}=9$$

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

$$8x+1=9$$

Subtract 1 from both sides.

$$8x=9-1$$

Subtract 1 from 9 to get 8.

$$8x=8$$

Divide both sides by 8.

$$x=\frac{8}{8}$$

Divide 8 by 8 to get 1.

$$x=1$$