Solve x^2+(k-2)x-2k=0

$$x ^ { 2 } + ( k - 2 ) x - 2 k = 0$$

Solve for k (complex solution)

$$\left\{\begin{matrix}\\k=-x\text{, }&\text{unconditionally}\\k\in \mathrm{C}\text{, }&x=2\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply k-2 by x.

$$x^{2}+kx-2x-2k=0$$

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

$$kx-2x-2k=-x^{2}$$

Add 2x to both sides.

$$kx-2k=-x^{2}+2x$$

Combine all terms containing k.

$$\left(x-2\right)k=-x^{2}+2x$$

The equation is in standard form.

$$\left(x-2\right)k=2x-x^{2}$$

Divide both sides by -2+x.

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

Dividing by -2+x undoes the multiplication by -2+x.

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

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

$$k=-x$$

Solve for k

$$\left\{\begin{matrix}\\k=-x\text{, }&\text{unconditionally}\\k\in \mathrm{R}\text{, }&x=2\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply k-2 by x.

$$x^{2}+kx-2x-2k=0$$

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

$$kx-2x-2k=-x^{2}$$

Add 2x to both sides.

$$kx-2k=-x^{2}+2x$$

Combine all terms containing k.

$$\left(x-2\right)k=-x^{2}+2x$$

The equation is in standard form.

$$\left(x-2\right)k=2x-x^{2}$$

Divide both sides by -2+x.

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

Dividing by -2+x undoes the multiplication by -2+x.

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

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

$$k=-x$$

Solve for x

$$x=-k$$

$$x=2$$