Solve x^2-2x-2n=0

$$x ^ { 2 } - 2 x - 2 n = 0$$

Solve for n

$$n=\frac{x\left(x-2\right)}{2}$$

Steps for Solving Linear Equation

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

$$-2x-2n=-x^{2}$$

Add 2x to both sides.

$$-2n=-x^{2}+2x$$

The equation is in standard form.

$$-2n=2x-x^{2}$$

Divide both sides by -2.

$$\frac{-2n}{-2}=\frac{x\left(2-x\right)}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$n=\frac{x\left(2-x\right)}{-2}$$

Divide x\left(2-x\right) by -2.

$$n=-\frac{x\left(2-x\right)}{2}$$

Solve for x (complex solution)

$$x=\sqrt{2n+1}+1$$

$$x=-\sqrt{2n+1}+1$$

Solve for x

$$x=\sqrt{2n+1}+1$$

$$x=-\sqrt{2n+1}+1\text{, }n\geq -\frac{1}{2}$$