Solve 0=25-16t^2

$$0 = 25-16 { t }^{ 2 }$$

Solve for t

$$t = \frac{5}{4} = 1\frac{1}{4} = 1.25$$

$$t = -\frac{5}{4} = -1\frac{1}{4} = -1.25$$

Steps by Finding Square Root

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

$$25-16t^{2}=0$$

Subtract 25 from both sides. Anything subtracted from zero gives its negation.

$$-16t^{2}=-25$$

Divide both sides by -16.

$$t^{2}=\frac{-25}{-16}$$

Fraction \frac{-25}{-16} can be simplified to \frac{25}{16} by removing the negative sign from both the numerator and the denominator.

$$t^{2}=\frac{25}{16}$$

Take the square root of both sides of the equation.

$$t=\frac{5}{4} t=-\frac{5}{4}$$

Steps Using the Quadratic Formula

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

$$25-16t^{2}=0$$

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.

$$-16t^{2}+25=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -16 for a, 0 for b, and 25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\left(-16\right)\times 25}}{2\left(-16\right)}$$

Square 0.

$$t=\frac{0±\sqrt{-4\left(-16\right)\times 25}}{2\left(-16\right)}$$

Multiply -4 times -16.

$$t=\frac{0±\sqrt{64\times 25}}{2\left(-16\right)}$$

Multiply 64 times 25.

$$t=\frac{0±\sqrt{1600}}{2\left(-16\right)}$$

Take the square root of 1600.

$$t=\frac{0±40}{2\left(-16\right)}$$

Multiply 2 times -16.

$$t=\frac{0±40}{-32}$$

Now solve the equation t=\frac{0±40}{-32} when ± is plus. Reduce the fraction \frac{40}{-32} to lowest terms by extracting and canceling out 8.

$$t=-\frac{5}{4}$$

Now solve the equation t=\frac{0±40}{-32} when ± is minus. Reduce the fraction \frac{-40}{-32} to lowest terms by extracting and canceling out 8.

$$t=\frac{5}{4}$$

The equation is now solved.

$$t=-\frac{5}{4} t=\frac{5}{4}$$