Solve x^2+2ax+1=0

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

Solve for a

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

$$x\neq 0$$

Steps for Solving Linear Equation

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

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

Subtract 1 from both sides.

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

The equation is in standard form.

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

Divide both sides by 2x.

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

Dividing by 2x undoes the multiplication by 2x.

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

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

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

Solve for x (complex solution)

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

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

Solve for x

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

$$x=-\sqrt{a^{2}-1}-a\text{, }|a|\geq 1$$