Solve a+1/a=0

$$a + \frac { 1 } { a } = 0$$

Solve for a

$$a=-i$$

$$a=i$$

Steps by Finding Square Root

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by a.

$$aa+1=0$$

Multiply a and a to get a^{2}.

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

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

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

The equation is now solved.

$$a=i a=-i$$

Steps Using the Quadratic Formula

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by a.

$$aa+1=0$$

Multiply a and a to get a^{2}.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4}}{2}$$

Take the square root of -4.

$$a=\frac{0±2i}{2}$$

Now solve the equation a=\frac{0±2i}{2} when ± is plus.

$$a=i$$

Now solve the equation a=\frac{0±2i}{2} when ± is minus.

$$a=-i$$

The equation is now solved.

$$a=i a=-i$$