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

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

Solve for x

$$x = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

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}.

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

Add 2 and 1 to get 3.

$$3+x^{2}+2x=x^{2}$$

Subtract x^{2} from both sides.

$$3+x^{2}+2x-x^{2}=0$$

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

$$3+2x=0$$

Subtract 3 from both sides. Anything subtracted from zero gives its negation.

$$2x=-3$$

Divide both sides by 2.

$$x=\frac{-3}{2}$$

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

$$x=-\frac{3}{2}$$