Solve kx^2-kx+1=0

$$k x ^ { 2 } - k x + 1 = 0$$

Solve for k

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

$$x\neq 1\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$kx^{2}-kx=-1$$

Combine all terms containing k.

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

Divide both sides by x^{2}-x.

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

Dividing by x^{2}-x undoes the multiplication by x^{2}-x.

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

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

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

Solve for x (complex solution)

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

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

Solve for x

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

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