Solve x^2+mx+2=0

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

Solve for m

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

$$x\neq 0$$

Steps for Solving Linear Equation

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

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

Subtract 2 from both sides.

$$mx=-x^{2}-2$$

The equation is in standard form.

$$xm=-x^{2}-2$$

Divide both sides by x.

$$\frac{xm}{x}=\frac{-x^{2}-2}{x}$$

Dividing by x undoes the multiplication by x.

$$m=\frac{-x^{2}-2}{x}$$

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

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

Solve for x (complex solution)

$$x=\frac{\sqrt{m^{2}-8}-m}{2}$$

$$x=\frac{-\sqrt{m^{2}-8}-m}{2}$$

Solve for x

$$x=\frac{\sqrt{m^{2}-8}-m}{2}$$

$$x=\frac{-\sqrt{m^{2}-8}-m}{2}\text{, }|m|\geq 2\sqrt{2}$$