Solve x^2+px+8=0

$$x ^ { 2 } + p x + 8 = 0$$

Solve for p

$$p=-x-\frac{8}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$px+8=-x^{2}$$

Subtract 8 from both sides.

$$px=-x^{2}-8$$

The equation is in standard form.

$$xp=-x^{2}-8$$

Divide both sides by x.

$$\frac{xp}{x}=\frac{-x^{2}-8}{x}$$

Dividing by x undoes the multiplication by x.

$$p=\frac{-x^{2}-8}{x}$$

Divide -x^{2}-8 by x.

$$p=-x-\frac{8}{x}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{p^{2}-32}-p}{2}$$

$$x=\frac{-\sqrt{p^{2}-32}-p}{2}$$

Solve for x

$$x=\frac{\sqrt{p^{2}-32}-p}{2}$$

$$x=\frac{-\sqrt{p^{2}-32}-p}{2}\text{, }|p|\geq 4\sqrt{2}$$