Solve 2x=x+1/x

$$2 x = x + \frac { 1 } { x }$$

Solve for x

$$x=-1$$

$$x=1$$

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.

$$2xx=xx+1$$

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

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

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

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

Subtract x^{2} from both sides.

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

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

$$x^{2}=1$$

Take the square root of both sides of the equation.

$$x=1 x=-1$$

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.

$$2xx=xx+1$$

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

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

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

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

Subtract x^{2} from both sides.

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

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

$$x^{2}=1$$

Subtract 1 from both sides.

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

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}.

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

Square 0.

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

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4}}{2}$$

Take the square root of 4.

$$x=\frac{0±2}{2}$$

Now solve the equation x=\frac{0±2}{2} when ± is plus. Divide 2 by 2.

$$x=1$$

Now solve the equation x=\frac{0±2}{2} when ± is minus. Divide -2 by 2.

$$x=-1$$

The equation is now solved.

$$x=1 x=-1$$