Solve 30000-30x^2=0

$$30000-30 { x }^{ 2 } = 0$$

Solve for x

$$x=10\sqrt{10}\approx 31.622776602$$

$$x=-10\sqrt{10}\approx -31.622776602$$

Steps by Finding Square Root

Subtract 30000 from both sides. Anything subtracted from zero gives its negation.

$$-30x^{2}=-30000$$

Divide both sides by -30.

$$x^{2}=\frac{-30000}{-30}$$

Divide -30000 by -30 to get 1000.

$$x^{2}=1000$$

Take the square root of both sides of the equation.

$$x=10\sqrt{10} x=-10\sqrt{10}$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-30x^{2}+30000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -30 for a, 0 for b, and 30000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-30\right)\times 30000}}{2\left(-30\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-30\right)\times 30000}}{2\left(-30\right)}$$

Multiply -4 times -30.

$$x=\frac{0±\sqrt{120\times 30000}}{2\left(-30\right)}$$

Multiply 120 times 30000.

$$x=\frac{0±\sqrt{3600000}}{2\left(-30\right)}$$

Take the square root of 3600000.

$$x=\frac{0±600\sqrt{10}}{2\left(-30\right)}$$

Multiply 2 times -30.

$$x=\frac{0±600\sqrt{10}}{-60}$$

Now solve the equation x=\frac{0±600\sqrt{10}}{-60} when ± is plus.

$$x=-10\sqrt{10}$$

Now solve the equation x=\frac{0±600\sqrt{10}}{-60} when ± is minus.

$$x=10\sqrt{10}$$

The equation is now solved.

$$x=-10\sqrt{10} x=10\sqrt{10}$$