Solve 2500-10t^2=0

$$2500 - 10 t ^ { 2 } = 0$$

Solve for t

$$t=5\sqrt{10}\approx 15.811388301$$

$$t=-5\sqrt{10}\approx -15.811388301$$

Steps by Finding Square Root

Subtract 2500 from both sides. Anything subtracted from zero gives its negation.

$$-10t^{2}=-2500$$

Divide both sides by -10.

$$t^{2}=\frac{-2500}{-10}$$

Divide -2500 by -10 to get 250.

$$t^{2}=250$$

Take the square root of both sides of the equation.

$$t=5\sqrt{10} t=-5\sqrt{10}$$

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.

$$-10t^{2}+2500=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -10 for a, 0 for b, and 2500 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\left(-10\right)\times 2500}}{2\left(-10\right)}$$

Square 0.

$$t=\frac{0±\sqrt{-4\left(-10\right)\times 2500}}{2\left(-10\right)}$$

Multiply -4 times -10.

$$t=\frac{0±\sqrt{40\times 2500}}{2\left(-10\right)}$$

Multiply 40 times 2500.

$$t=\frac{0±\sqrt{100000}}{2\left(-10\right)}$$

Take the square root of 100000.

$$t=\frac{0±100\sqrt{10}}{2\left(-10\right)}$$

Multiply 2 times -10.

$$t=\frac{0±100\sqrt{10}}{-20}$$

Now solve the equation t=\frac{0±100\sqrt{10}}{-20} when ± is plus.

$$t=-5\sqrt{10}$$

Now solve the equation t=\frac{0±100\sqrt{10}}{-20} when ± is minus.

$$t=5\sqrt{10}$$

The equation is now solved.

$$t=-5\sqrt{10} t=5\sqrt{10}$$