Solve x=x^2*1/2499

$$x= { x }^{ 2 } \times \frac{ 1 }{ 2499 }$$

Solve for x

$$x=2499$$

$$x=0$$

Steps Using Factoring

Subtract x^{2}\times \frac{1}{2499} from both sides.

$$x-x^{2}\times \frac{1}{2499}=0$$

Multiply -1 and \frac{1}{2499} to get -\frac{1}{2499}.

$$x-\frac{1}{2499}x^{2}=0$$

Factor out x.

$$x\left(1-\frac{1}{2499}x\right)=0$$

To find equation solutions, solve x=0 and 1-\frac{x}{2499}=0.

$$x=0 x=2499$$

Steps Using the Quadratic Formula

Subtract x^{2}\times \frac{1}{2499} from both sides.

$$x-x^{2}\times \frac{1}{2499}=0$$

Multiply -1 and \frac{1}{2499} to get -\frac{1}{2499}.

$$x-\frac{1}{2499}x^{2}=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$-\frac{1}{2499}x^{2}+x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -\frac{1}{2499} for a, 1 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-1±\sqrt{1^{2}}}{2\left(-\frac{1}{2499}\right)}$$

Take the square root of 1^{2}.

$$x=\frac{-1±1}{2\left(-\frac{1}{2499}\right)}$$

Multiply 2 times -\frac{1}{2499}.

$$x=\frac{-1±1}{-\frac{2}{2499}}$$

Now solve the equation x=\frac{-1±1}{-\frac{2}{2499}} when ± is plus. Add -1 to 1.

$$x=\frac{0}{-\frac{2}{2499}}$$

Divide 0 by -\frac{2}{2499} by multiplying 0 by the reciprocal of -\frac{2}{2499}.

$$x=0$$

Now solve the equation x=\frac{-1±1}{-\frac{2}{2499}} when ± is minus. Subtract 1 from -1.

$$x=-\frac{2}{-\frac{2}{2499}}$$

Divide -2 by -\frac{2}{2499} by multiplying -2 by the reciprocal of -\frac{2}{2499}.

$$x=2499$$

The equation is now solved.

$$x=0 x=2499$$

Steps for Completing the Square

Subtract x^{2}\times \frac{1}{2499} from both sides.

$$x-x^{2}\times \frac{1}{2499}=0$$

Multiply -1 and \frac{1}{2499} to get -\frac{1}{2499}.

$$x-\frac{1}{2499}x^{2}=0$$

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

$$-\frac{1}{2499}x^{2}+x=0$$

Multiply both sides by -2499.

$$\frac{-\frac{1}{2499}x^{2}+x}{-\frac{1}{2499}}=\frac{0}{-\frac{1}{2499}}$$

Dividing by -\frac{1}{2499} undoes the multiplication by -\frac{1}{2499}.

$$x^{2}+\frac{1}{-\frac{1}{2499}}x=\frac{0}{-\frac{1}{2499}}$$

Divide 1 by -\frac{1}{2499} by multiplying 1 by the reciprocal of -\frac{1}{2499}.

$$x^{2}-2499x=\frac{0}{-\frac{1}{2499}}$$

Divide 0 by -\frac{1}{2499} by multiplying 0 by the reciprocal of -\frac{1}{2499}.

$$x^{2}-2499x=0$$

Divide -2499, the coefficient of the x term, by 2 to get -\frac{2499}{2}. Then add the square of -\frac{2499}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-2499x+\left(-\frac{2499}{2}\right)^{2}=\left(-\frac{2499}{2}\right)^{2}$$

Square -\frac{2499}{2} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-2499x+\frac{6245001}{4}=\frac{6245001}{4}$$

Factor x^{2}-2499x+\frac{6245001}{4}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{2499}{2}\right)^{2}=\frac{6245001}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{2499}{2}\right)^{2}}=\sqrt{\frac{6245001}{4}}$$

Simplify.

$$x-\frac{2499}{2}=\frac{2499}{2} x-\frac{2499}{2}=-\frac{2499}{2}$$

Add \frac{2499}{2} to both sides of the equation.

$$x=2499 x=0$$