Solve x^2+ax+8a=0

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

Solve for a

$$a=-\frac{x^{2}}{x+8}$$

$$x\neq -8$$

Steps for Solving Linear Equation

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

$$ax+8a=-x^{2}$$

Combine all terms containing a.

$$\left(x+8\right)a=-x^{2}$$

Divide both sides by x+8.

$$\frac{\left(x+8\right)a}{x+8}=-\frac{x^{2}}{x+8}$$

Dividing by x+8 undoes the multiplication by x+8.

$$a=-\frac{x^{2}}{x+8}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{a\left(a-32\right)}-a}{2}$$

$$x=\frac{-\sqrt{a\left(a-32\right)}-a}{2}$$

Solve for x

$$x=\frac{\sqrt{a\left(a-32\right)}-a}{2}$$

$$x=\frac{-\sqrt{a\left(a-32\right)}-a}{2}\text{, }a\geq 32\text{ or }a\leq 0$$