Solve x/2=x/2-x

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

Solve for x

$$x=0$$

Steps by Finding Square Root

Variable x cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by 2\left(x-2\right), the least common multiple of 2,2-x.

$$\left(x-2\right)x=-2x$$

Use the distributive property to multiply x-2 by x.

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

Add 2x to both sides.

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

Combine -2x and 2x to get 0.

$$x^{2}=0$$

Take the square root of both sides of the equation.

$$x=0 x=0$$

The equation is now solved. Solutions are the same.

$$x=0$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by 2\left(x-2\right), the least common multiple of 2,2-x.

$$\left(x-2\right)x=-2x$$

Use the distributive property to multiply x-2 by x.

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

Add 2x to both sides.

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

Combine -2x and 2x to get 0.

$$x^{2}=0$$

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

$$x=\frac{0±\sqrt{0^{2}}}{2}$$

Take the square root of 0^{2}.

$$x=\frac{0±0}{2}$$

Divide 0 by 2.

$$x=0$$