Solve x+1/x=4x

$$x + \frac { 1 } { x } = 4 x$$

Solve for x

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

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

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.

$$xx+1=4xx$$

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

$$x^{2}+1=4xx$$

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

$$x^{2}+1=4x^{2}$$

Subtract 4x^{2} from both sides.

$$x^{2}+1-4x^{2}=0$$

Combine x^{2} and -4x^{2} to get -3x^{2}.

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

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

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

Divide both sides by -3.

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

Fraction \frac{-1}{-3} can be simplified to \frac{1}{3} by removing the negative sign from both the numerator and the denominator.

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

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

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

$$xx+1=4xx$$

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

$$x^{2}+1=4xx$$

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

$$x^{2}+1=4x^{2}$$

Subtract 4x^{2} from both sides.

$$x^{2}+1-4x^{2}=0$$

Combine x^{2} and -4x^{2} to get -3x^{2}.

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

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}.

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

Square 0.

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

Multiply -4 times -3.

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

Take the square root of 12.

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

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.

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