Solve x^2+2dx+1=0

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

Solve for d

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

$$x\neq 0$$

Steps for Solving Linear Equation

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

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

Subtract 1 from both sides.

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

The equation is in standard form.

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

Divide both sides by 2x.

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

Dividing by 2x undoes the multiplication by 2x.

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

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

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

Solve for x (complex solution)

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

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

Solve for x

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

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