Solve 003=100x-41666662x^2

$$003 = 100 x - 41666662 x ^ { 2 }$$

Solve for x

$$x=\frac{50}{20833331}\approx 0.0000024$$

$$x=0$$

Steps Using Factoring

Multiply 0 and 0 to get 0.

$$0\times 3=100x-41666662x^{2}$$

Multiply 0 and 3 to get 0.

$$0=100x-41666662x^{2}$$

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

$$100x-41666662x^{2}=0$$

Factor out x.

$$x\left(100-41666662x\right)=0$$

To find equation solutions, solve x=0 and 100-41666662x=0.

$$x=0 x=\frac{50}{20833331}$$

Steps Using the Quadratic Formula

Multiply 0 and 0 to get 0.

$$0\times 3=100x-41666662x^{2}$$

Multiply 0 and 3 to get 0.

$$0=100x-41666662x^{2}$$

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

$$100x-41666662x^{2}=0$$

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.

$$-41666662x^{2}+100x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -41666662 for a, 100 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-100±\sqrt{100^{2}}}{2\left(-41666662\right)}$$

Take the square root of 100^{2}.

$$x=\frac{-100±100}{2\left(-41666662\right)}$$

Multiply 2 times -41666662.

$$x=\frac{-100±100}{-83333324}$$

Now solve the equation x=\frac{-100±100}{-83333324} when ± is plus. Add -100 to 100.

$$x=\frac{0}{-83333324}$$

Divide 0 by -83333324.

$$x=0$$

Now solve the equation x=\frac{-100±100}{-83333324} when ± is minus. Subtract 100 from -100.

$$x=-\frac{200}{-83333324}$$

Reduce the fraction \frac{-200}{-83333324} to lowest terms by extracting and canceling out 4.

$$x=\frac{50}{20833331}$$

The equation is now solved.

$$x=0 x=\frac{50}{20833331}$$

Steps for Completing the Square

Multiply 0 and 0 to get 0.

$$0\times 3=100x-41666662x^{2}$$

Multiply 0 and 3 to get 0.

$$0=100x-41666662x^{2}$$

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

$$100x-41666662x^{2}=0$$

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.

$$-41666662x^{2}+100x=0$$

Divide both sides by -41666662.

$$\frac{-41666662x^{2}+100x}{-41666662}=\frac{0}{-41666662}$$

Dividing by -41666662 undoes the multiplication by -41666662.

$$x^{2}+\frac{100}{-41666662}x=\frac{0}{-41666662}$$

Reduce the fraction \frac{100}{-41666662} to lowest terms by extracting and canceling out 2.

$$x^{2}-\frac{50}{20833331}x=\frac{0}{-41666662}$$

Divide 0 by -41666662.

$$x^{2}-\frac{50}{20833331}x=0$$

Divide -\frac{50}{20833331}, the coefficient of the x term, by 2 to get -\frac{25}{20833331}. Then add the square of -\frac{25}{20833331} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{50}{20833331}x+\left(-\frac{25}{20833331}\right)^{2}=\left(-\frac{25}{20833331}\right)^{2}$$

Square -\frac{25}{20833331} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{50}{20833331}x+\frac{625}{434027680555561}=\frac{625}{434027680555561}$$

Factor x^{2}-\frac{50}{20833331}x+\frac{625}{434027680555561}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{25}{20833331}\right)^{2}=\frac{625}{434027680555561}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{25}{20833331}\right)^{2}}=\sqrt{\frac{625}{434027680555561}}$$

Simplify.

$$x-\frac{25}{20833331}=\frac{25}{20833331} x-\frac{25}{20833331}=-\frac{25}{20833331}$$

Add \frac{25}{20833331} to both sides of the equation.

$$x=\frac{50}{20833331} x=0$$