Solve -1/x-x=0

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

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.

$$-1-xx=0$$

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

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

Add 1 to both sides. Anything plus zero gives itself.

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

Divide both sides by -1.

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

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.

$$-1-xx=0$$

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

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

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

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

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}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\left(-1\right)}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\left(-1\right)}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\left(-1\right)}}{2\left(-1\right)}$$

Multiply 4 times -1.

$$x=\frac{0±\sqrt{-4}}{2\left(-1\right)}$$

Take the square root of -4.

$$x=\frac{0±2i}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±2i}{-2}$$

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.

$$x=-i x=i$$