Solve 2/x-2/2x=x

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

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 2x, the least common multiple of x,2x.

$$2\times 2-2=x\times 2x$$

Multiply 2 and 2 to get 4.

$$4-2=x\times 2x$$

Subtract 2 from 4 to get 2.

$$2=x\times 2x$$

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

$$2=x^{2}\times 2$$

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

$$x^{2}\times 2=2$$

Divide both sides by 2.

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

Divide 2 by 2 to get 1.

$$x^{2}=1$$

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 2x, the least common multiple of x,2x.

$$2\times 2-2=x\times 2x$$

Multiply 2 and 2 to get 4.

$$4-2=x\times 2x$$

Subtract 2 from 4 to get 2.

$$2=x\times 2x$$

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

$$2=x^{2}\times 2$$

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

$$x^{2}\times 2=2$$

Subtract 2 from both sides.

$$x^{2}\times 2-2=0$$

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.

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

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

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

Square 0.

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

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-2\right)}}{2\times 2}$$

Multiply -8 times -2.

$$x=\frac{0±\sqrt{16}}{2\times 2}$$

Take the square root of 16.

$$x=\frac{0±4}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±4}{4}$$

Now solve the equation x=\frac{0±4}{4} when ± is plus. Divide 4 by 4.

$$x=1$$

Now solve the equation x=\frac{0±4}{4} when ± is minus. Divide -4 by 4.

$$x=-1$$

The equation is now solved.

$$x=1 x=-1$$