Solve x^2-kx+phi=0

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

Solve for k (complex solution)

$$\left\{\begin{matrix}k=x+\frac{ϕ}{x}\text{, }&x\neq 0\\k\in \mathrm{C}\text{, }&ϕ=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$-kx+ϕ=-x^{2}$$

Subtract ϕ from both sides.

$$-kx=-x^{2}-ϕ$$

The equation is in standard form.

$$\left(-x\right)k=-x^{2}-ϕ$$

Divide both sides by -x.

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

Dividing by -x undoes the multiplication by -x.

$$k=\frac{-x^{2}-ϕ}{-x}$$

Divide -x^{2}-ϕ by -x.

$$k=x+\frac{ϕ}{x}$$

Solve for k

$$\left\{\begin{matrix}k=x+\frac{ϕ}{x}\text{, }&x\neq 0\\k\in \mathrm{R}\text{, }&ϕ=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$-kx+ϕ=-x^{2}$$

Subtract ϕ from both sides.

$$-kx=-x^{2}-ϕ$$

The equation is in standard form.

$$\left(-x\right)k=-x^{2}-ϕ$$

Divide both sides by -x.

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

Dividing by -x undoes the multiplication by -x.

$$k=\frac{-x^{2}-ϕ}{-x}$$

Divide -x^{2}-ϕ by -x.

$$k=x+\frac{ϕ}{x}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{k^{2}-4ϕ}+k}{2}$$

$$x=\frac{-\sqrt{k^{2}-4ϕ}+k}{2}$$

Solve for x

$$x=\frac{\sqrt{k^{2}-4ϕ}+k}{2}$$

$$x=\frac{-\sqrt{k^{2}-4ϕ}+k}{2}\text{, }ϕ\leq \frac{k^{2}}{4}$$