Solve (x+1)^2=x^2-7x

$$( x + 1 ) ^ { 2 } = x ^ { 2 } - 7 x$$

Solve for x

$$x=-\frac{1}{9}\approx -0.111111111$$

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}.

$$x^{2}+2x+1=x^{2}-7x$$

Subtract x^{2} from both sides.

$$x^{2}+2x+1-x^{2}=-7x$$

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

$$2x+1=-7x$$

Add 7x to both sides.

$$2x+1+7x=0$$

Combine 2x and 7x to get 9x.

$$9x+1=0$$

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$9x=-1$$

Divide both sides by 9.

$$x=\frac{-1}{9}$$

Fraction \frac{-1}{9} can be rewritten as -\frac{1}{9} by extracting the negative sign.

$$x=-\frac{1}{9}$$