Solve x+1/x+2/x=0

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

Solve for x (complex solution)

$$x=-\sqrt{3}i\approx -0-1.732050808i$$

$$x=\sqrt{3}i\approx 1.732050808i$$

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.

$$xx+1+2=0$$

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

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

Add 1 and 2 to get 3.

$$x^{2}+3=0$$

Subtract 3 from both sides. Anything subtracted from zero gives its negation.

$$x^{2}=-3$$

The equation is now solved.

$$x=\sqrt{3}i x=-\sqrt{3}i$$

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.

$$xx+1+2=0$$

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

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

Add 1 and 2 to get 3.

$$x^{2}+3=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 3 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3}}{2}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12}}{2}$$

Take the square root of -12.

$$x=\frac{0±2\sqrt{3}i}{2}$$

Now solve the equation x=\frac{0±2\sqrt{3}i}{2} when ± is plus.

$$x=\sqrt{3}i$$

Now solve the equation x=\frac{0±2\sqrt{3}i}{2} when ± is minus.

$$x=-\sqrt{3}i$$

The equation is now solved.

$$x=\sqrt{3}i x=-\sqrt{3}i$$