Solve -1/5x=2x

$$- \frac { 1 } { 5 x } = 2 x$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{10}i}{10}\approx -0-0.316227766i$$

$$x=\frac{\sqrt{10}i}{10}\approx 0.316227766i$$

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 5x.

$$-1=2x\times 5x$$

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

$$-1=2x^{2}\times 5$$

Multiply 2 and 5 to get 10.

$$-1=10x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$10x^{2}=-1$$

Divide both sides by 10.

$$x^{2}=-\frac{1}{10}$$

The equation is now solved.

$$x=\frac{\sqrt{10}i}{10} x=-\frac{\sqrt{10}i}{10}$$

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 5x.

$$-1=2x\times 5x$$

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

$$-1=2x^{2}\times 5$$

Multiply 2 and 5 to get 10.

$$-1=10x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$10x^{2}=-1$$

Add 1 to both sides.

$$10x^{2}+1=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 10 for a, 0 for b, and 1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 10}}{2\times 10}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 10}}{2\times 10}$$

Multiply -4 times 10.

$$x=\frac{0±\sqrt{-40}}{2\times 10}$$

Take the square root of -40.

$$x=\frac{0±2\sqrt{10}i}{2\times 10}$$

Multiply 2 times 10.

$$x=\frac{0±2\sqrt{10}i}{20}$$

Now solve the equation x=\frac{0±2\sqrt{10}i}{20} when ± is plus.

$$x=\frac{\sqrt{10}i}{10}$$

Now solve the equation x=\frac{0±2\sqrt{10}i}{20} when ± is minus.

$$x=-\frac{\sqrt{10}i}{10}$$

The equation is now solved.

$$x=\frac{\sqrt{10}i}{10} x=-\frac{\sqrt{10}i}{10}$$