Solve x^2+alphax+1=0

$$x ^ { 2 } + \alpha x + 1 = 0$$

Solve for α

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

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$\alpha x+1=-x^{2}$$

Subtract 1 from both sides.

$$\alpha x=-x^{2}-1$$

The equation is in standard form.

$$x\alpha =-x^{2}-1$$

Divide both sides by x.

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

Dividing by x undoes the multiplication by x.

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

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

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

Solve for x (complex solution)

$$x=\frac{\sqrt{\alpha ^{2}-4}-\alpha }{2}$$

$$x=\frac{-\sqrt{\alpha ^{2}-4}-\alpha }{2}$$

Solve for x

$$x=\frac{\sqrt{\alpha ^{2}-4}-\alpha }{2}$$

$$x=\frac{-\sqrt{\alpha ^{2}-4}-\alpha }{2}\text{, }|\alpha |\geq 2$$