Solve c^2+(k-1)x+4=0

$$c ^ { 2 } + ( k - 1 ) x + 4 = 0$$

Solve for k (complex solution)

$$\left\{\begin{matrix}k=-\frac{4+c^{2}-x}{x}\text{, }&x\neq 0\\k\in \mathrm{C}\text{, }&\left(c=2i\text{ or }c=-2i\right)\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply k-1 by x.

$$c^{2}+kx-x+4=0$$

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

$$kx-x+4=-c^{2}$$

Add x to both sides.

$$kx+4=-c^{2}+x$$

Subtract 4 from both sides.

$$kx=-c^{2}+x-4$$

The equation is in standard form.

$$xk=x-c^{2}-4$$

Divide both sides by x.

$$\frac{xk}{x}=\frac{x-c^{2}-4}{x}$$

Dividing by x undoes the multiplication by x.

$$k=\frac{x-c^{2}-4}{x}$$

Solve for k

$$k=-\frac{4+c^{2}-x}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply k-1 by x.

$$c^{2}+kx-x+4=0$$

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

$$kx-x+4=-c^{2}$$

Add x to both sides.

$$kx+4=-c^{2}+x$$

Subtract 4 from both sides.

$$kx=-c^{2}+x-4$$

The equation is in standard form.

$$xk=x-c^{2}-4$$

Divide both sides by x.

$$\frac{xk}{x}=\frac{x-c^{2}-4}{x}$$

Dividing by x undoes the multiplication by x.

$$k=\frac{x-c^{2}-4}{x}$$

Solve for c (complex solution)

$$c=-\sqrt{-kx+x-4}$$

$$c=\sqrt{-kx+x-4}$$

Solve for c

$$c=\sqrt{-kx+x-4}$$

$$c=-\sqrt{-kx+x-4}\text{, }\left(x>0\text{ or }k\geq \frac{x-4}{x}\right)\text{ and }\left(x<0\text{ or }k\leq \frac{x-4}{x}\right)\text{ and }x\neq 0$$