Solve 1/x+9x=0

$$\frac{ 1 }{ x } +9x=0$$

Solve for x (complex solution)

$$x=\frac{1}{3}i\approx 0.333333333i$$

$$x=-\frac{1}{3}i\approx -0.333333333i$$

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.

$$1+9xx=0$$

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

$$1+9x^{2}=0$$

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

$$9x^{2}=-1$$

Divide both sides by 9.

$$x^{2}=-\frac{1}{9}$$

The equation is now solved.

$$x=\frac{1}{3}i x=-\frac{1}{3}i$$

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.

$$1+9xx=0$$

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

$$1+9x^{2}=0$$

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.

$$9x^{2}+1=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 9 for a, 0 for b, and 1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 9}}{2\times 9}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 9}}{2\times 9}$$

Multiply -4 times 9.

$$x=\frac{0±\sqrt{-36}}{2\times 9}$$

Take the square root of -36.

$$x=\frac{0±6i}{2\times 9}$$

Multiply 2 times 9.

$$x=\frac{0±6i}{18}$$

Now solve the equation x=\frac{0±6i}{18} when ± is plus.

$$x=\frac{1}{3}i$$

Now solve the equation x=\frac{0±6i}{18} when ± is minus.

$$x=-\frac{1}{3}i$$

The equation is now solved.

$$x=\frac{1}{3}i x=-\frac{1}{3}i$$