Solve x^2+ax+1=0

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

Solve for a

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

$$x\neq 0$$

Steps for Solving Linear Equation

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

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

Subtract 1 from both sides.

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

The equation is in standard form.

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

Divide both sides by x.

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

Dividing by x undoes the multiplication by x.

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

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

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

Solve for x (complex solution)

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

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

Solve for x

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

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