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

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

Solve for k (complex solution)

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

Steps for Solving Linear Equation

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

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

Add 2 to both sides.

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

Combine all terms containing k.

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

The equation is in standard form.

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

Divide both sides by 1+x.

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

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

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

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

$$k=2-2x$$

Solve for k

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

Steps for Solving Linear Equation

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

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

Add 2 to both sides.

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

Combine all terms containing k.

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

The equation is in standard form.

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

Divide both sides by 1+x.

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

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

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

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

$$k=2-2x$$

Solve for x

$$x=-1$$

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