Solve x^2+(m+1)x+2m+2=0

$$x ^ { 2 } + ( m + 1 ) x + 2 m + 2 = 0$$

Solve for m

$$m=\frac{-x^{2}-x-2}{x+2}$$

$$x\neq -2$$

Steps for Solving Linear Equation

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

$$x^{2}+mx+x+2m+2=0$$

Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.

$$mx+x+2m+2=-x^{2}$$

Subtract x from both sides.

$$mx+2m+2=-x^{2}-x$$

Subtract 2 from both sides.

$$mx+2m=-x^{2}-x-2$$

Combine all terms containing m.

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

Divide both sides by x+2.

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

Dividing by x+2 undoes the multiplication by x+2.

$$m=\frac{-x^{2}-x-2}{x+2}$$

Divide -x^{2}-x-2 by x+2.

$$m=-\frac{x^{2}+x+2}{x+2}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{\left(m-7\right)\left(m+1\right)}-m-1}{2}$$

$$x=\frac{-\sqrt{\left(m-7\right)\left(m+1\right)}-m-1}{2}$$

Solve for x

$$x=\frac{\sqrt{\left(m-7\right)\left(m+1\right)}-m-1}{2}$$

$$x=\frac{-\sqrt{\left(m-7\right)\left(m+1\right)}-m-1}{2}\text{, }m\leq -1\text{ or }m\geq 7$$