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

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

Solve for u

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

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$x^{2}+ux+x+1=0$$

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

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

Subtract x from both sides.

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

Subtract 1 from both sides.

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

The equation is in standard form.

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

Divide both sides by x.

$$\frac{xu}{x}=\frac{-x^{2}-x-1}{x}$$

Dividing by x undoes the multiplication by x.

$$u=\frac{-x^{2}-x-1}{x}$$

Divide -x^{2}-x-1 by x.

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

Solve for x (complex solution)

$$x=\frac{\sqrt{\left(u-1\right)\left(u+3\right)}-u-1}{2}$$

$$x=\frac{-\sqrt{\left(u-1\right)\left(u+3\right)}-u-1}{2}$$

Solve for x

$$x=\frac{\sqrt{\left(u-1\right)\left(u+3\right)}-u-1}{2}$$

$$x=\frac{-\sqrt{\left(u-1\right)\left(u+3\right)}-u-1}{2}\text{, }u\leq -3\text{ or }u\geq 1$$