Solve x^2+kx-k=0

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

Solve for k

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

$$x\neq 1$$

Steps for Solving Linear Equation

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

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

Combine all terms containing k.

$$\left(x-1\right)k=-x^{2}$$

Divide both sides by x-1.

$$\frac{\left(x-1\right)k}{x-1}=-\frac{x^{2}}{x-1}$$

Dividing by x-1 undoes the multiplication by x-1.

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

Solve for x (complex solution)

$$x=\frac{\sqrt{k\left(k+4\right)}-k}{2}$$

$$x=\frac{-\sqrt{k\left(k+4\right)}-k}{2}$$

Solve for x

$$x=\frac{\sqrt{k\left(k+4\right)}-k}{2}$$

$$x=\frac{-\sqrt{k\left(k+4\right)}-k}{2}\text{, }k\leq -4\text{ or }k\geq 0$$