Solve (x)=100x/100-x^2/1000

$$( x ) = 100 \frac { x } { 100 } - \frac { x ^ { 2 } } { 1000 }$$

Solve for x

$$x=0$$

Steps by Finding Square Root

Express 100\times \frac{x}{100} as a single fraction.

$$x=\frac{100x}{100}-\frac{x^{2}}{1000}$$

Cancel out 100 and 100.

$$x=x-\frac{x^{2}}{1000}$$

Subtract x from both sides.

$$x-x=-\frac{x^{2}}{1000}$$

Combine x and -x to get 0.

$$0=-\frac{x^{2}}{1000}$$

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

$$-\frac{x^{2}}{1000}=0$$

Multiply both sides of the equation by 1000.

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

Divide both sides by -1. Zero divided by any non-zero number gives zero.

$$x^{2}=0$$

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

Express 100\times \frac{x}{100} as a single fraction.

$$x=\frac{100x}{100}-\frac{x^{2}}{1000}$$

Cancel out 100 and 100.

$$x=x-\frac{x^{2}}{1000}$$

Subtract x from both sides.

$$x-x=-\frac{x^{2}}{1000}$$

Combine x and -x to get 0.

$$0=-\frac{x^{2}}{1000}$$

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

$$-\frac{x^{2}}{1000}=0$$

Multiply both sides of the equation by 1000.

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

Divide both sides by -1. Zero divided by any non-zero number gives zero.

$$x^{2}=0$$

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.

$$x=0$$