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

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

Solve for x

$$x=-1$$

Steps for Solving Linear Equation

Use the distributive property to multiply x by x+1.

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

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

$$x^{2}+x+1=x^{2}+4x+4$$

Subtract x^{2} from both sides.

$$x^{2}+x+1-x^{2}=4x+4$$

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

$$x+1=4x+4$$

Subtract 4x from both sides.

$$x+1-4x=4$$

Combine x and -4x to get -3x.

$$-3x+1=4$$

Subtract 1 from both sides.

$$-3x=4-1$$

Subtract 1 from 4 to get 3.

$$-3x=3$$

Divide both sides by -3.

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

Divide 3 by -3 to get -1.

$$x=-1$$