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

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

Solve for k (complex solution)

$$\left\{\begin{matrix}k=-\frac{2}{x}\text{, }&x\neq 0\\k\in \mathrm{C}\text{, }&x=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

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

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

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

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

Subtract 2 from both sides.

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

Combine all terms containing k.

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

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

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

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

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

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

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

Solve for k

$$\left\{\begin{matrix}k=-\frac{2}{x}\text{, }&x\neq 0\\k\in \mathrm{R}\text{, }&x=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

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

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

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

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

Subtract 2 from both sides.

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

Combine all terms containing k.

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

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

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

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

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

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

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

Solve for x

$$\left\{\begin{matrix}\\x=-1\text{, }&\text{unconditionally}\\x=-\frac{2}{k}\text{, }&k\neq 0\end{matrix}\right.$$