Solve left(x+1right)^2=x^2-1

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

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}.

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

Subtract x^{2} from both sides.

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

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

$$2x+1=-1$$

Subtract 1 from both sides.

$$2x=-1-1$$

Subtract 1 from -1 to get -2.

$$2x=-2$$

Divide both sides by 2.

$$x=\frac{-2}{2}$$

Divide -2 by 2 to get -1.

$$x=-1$$