Solve x=1/3x

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

Solve for x

$$x=\frac{\sqrt{3}}{3}\approx 0.577350269$$

$$x=-\frac{\sqrt{3}}{3}\approx -0.577350269$$

Steps by Finding Square Root

Subtract \frac{1}{3x} from both sides.

$$x-\frac{1}{3x}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{3x}{3x}.

$$\frac{x\times 3x}{3x}-\frac{1}{3x}=0$$

Since \frac{x\times 3x}{3x} and \frac{1}{3x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x\times 3x-1}{3x}=0$$

Do the multiplications in x\times 3x-1.

$$\frac{3x^{2}-1}{3x}=0$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 3x.

$$3x^{2}-1=0$$

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

$$3x^{2}=1$$

Divide both sides by 3.

$$x^{2}=\frac{1}{3}$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Subtract \frac{1}{3x} from both sides.

$$x-\frac{1}{3x}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{3x}{3x}.

$$\frac{x\times 3x}{3x}-\frac{1}{3x}=0$$

Since \frac{x\times 3x}{3x} and \frac{1}{3x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x\times 3x-1}{3x}=0$$

Do the multiplications in x\times 3x-1.

$$\frac{3x^{2}-1}{3x}=0$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 3x.

$$3x^{2}-1=0$$

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

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-1\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-1\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-1\right)}}{2\times 3}$$

Multiply -12 times -1.

$$x=\frac{0±\sqrt{12}}{2\times 3}$$

Take the square root of 12.

$$x=\frac{0±2\sqrt{3}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±2\sqrt{3}}{6}$$

Now solve the equation x=\frac{0±2\sqrt{3}}{6} when ± is plus.

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

Now solve the equation x=\frac{0±2\sqrt{3}}{6} when ± is minus.

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

The equation is now solved.

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