Solve 800x^2-60000x=0

$$800 x ^ { 2 } - 60000 x = 0$$

Solve for x

$$x=75$$

$$x=0$$

Steps Using Factoring

Factor out x.

$$x\left(800x-60000\right)=0$$

To find equation solutions, solve x=0 and 800x-60000=0.

$$x=0 x=75$$

Steps Using the Quadratic Formula

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.

$$800x^{2}-60000x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 800 for a, -60000 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-60000\right)±\sqrt{\left(-60000\right)^{2}}}{2\times 800}$$

Take the square root of \left(-60000\right)^{2}.

$$x=\frac{-\left(-60000\right)±60000}{2\times 800}$$

The opposite of -60000 is 60000.

$$x=\frac{60000±60000}{2\times 800}$$

Multiply 2 times 800.

$$x=\frac{60000±60000}{1600}$$

Now solve the equation x=\frac{60000±60000}{1600} when ± is plus. Add 60000 to 60000.

$$x=\frac{120000}{1600}$$

Divide 120000 by 1600.

$$x=75$$

Now solve the equation x=\frac{60000±60000}{1600} when ± is minus. Subtract 60000 from 60000.

$$x=\frac{0}{1600}$$

Divide 0 by 1600.

$$x=0$$

The equation is now solved.

$$x=75 x=0$$

Steps for Completing the Square

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.

$$800x^{2}-60000x=0$$

Divide both sides by 800.

$$\frac{800x^{2}-60000x}{800}=\frac{0}{800}$$

Dividing by 800 undoes the multiplication by 800.

$$x^{2}+\left(-\frac{60000}{800}\right)x=\frac{0}{800}$$

Divide -60000 by 800.

$$x^{2}-75x=\frac{0}{800}$$

Divide 0 by 800.

$$x^{2}-75x=0$$

Divide -75, the coefficient of the x term, by 2 to get -\frac{75}{2}. Then add the square of -\frac{75}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-75x+\left(-\frac{75}{2}\right)^{2}=\left(-\frac{75}{2}\right)^{2}$$

Square -\frac{75}{2} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-75x+\frac{5625}{4}=\frac{5625}{4}$$

Factor x^{2}-75x+\frac{5625}{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}.

$$\left(x-\frac{75}{2}\right)^{2}=\frac{5625}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{75}{2}\right)^{2}}=\sqrt{\frac{5625}{4}}$$

Simplify.

$$x-\frac{75}{2}=\frac{75}{2} x-\frac{75}{2}=-\frac{75}{2}$$

Add \frac{75}{2} to both sides of the equation.

$$x=75 x=0$$