Solve 2ax^2+1/x=0

$$\frac { 2 a x ^ { 2 } + 1 } { x } = 0$$

Solve for a

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

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$2ax^{2}+1=0$$

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$2ax^{2}=-1$$

The equation is in standard form.

$$2x^{2}a=-1$$

Divide both sides by 2x^{2}.

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

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

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

Solve for x (complex solution)

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

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

Solve for x

$$x=\frac{\sqrt{-\frac{2}{a}}}{2}$$

$$x=-\frac{\sqrt{-\frac{2}{a}}}{2}\text{, }a<0$$