Solve ax^2+ax+2=0

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

Solve for a

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

$$x\neq -1\text{ and }x\neq 0$$

Steps for Solving Linear Equation

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

$$ax^{2}+ax=-2$$

Combine all terms containing a.

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

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

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

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

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

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

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

Solve for x (complex solution)

$$x=\frac{\sqrt{a^{2}-8a}}{2a}-\frac{1}{2}$$

$$x=-\frac{\sqrt{a^{2}-8a}}{2a}-\frac{1}{2}\text{, }a\neq 0$$

Solve for x

$$x=\frac{\sqrt{a^{2}-8a}}{2a}-\frac{1}{2}$$

$$x=-\frac{\sqrt{a^{2}-8a}}{2a}-\frac{1}{2}\text{, }a<0\text{ or }a\geq 8$$