Solve x+1/x=0

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

Solve for x (complex solution)

$$x=-i$$

$$x=i$$

Steps by Finding Square Root

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

$$xx+1=0$$

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

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

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

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

The equation is now solved.

$$x=i x=-i$$

Steps Using the Quadratic Formula

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

$$xx+1=0$$

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

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

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}.

$$x=\frac{0±\sqrt{0^{2}-4}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4}}{2}$$

Take the square root of -4.

$$x=\frac{0±2i}{2}$$

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

$$x=i$$

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

$$x=-i$$

The equation is now solved.

$$x=i x=-i$$