Solve 1=5-16t^2

$$1 = 5 - 16 t ^ { 2 }$$

Solve for t

$$t=\frac{1}{2}=0.5$$

$$t=-\frac{1}{2}=-0.5$$

Steps by Finding Square Root

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

$$5-16t^{2}=1$$

Subtract 5 from both sides.

$$-16t^{2}=1-5$$

Subtract 5 from 1 to get -4.

$$-16t^{2}=-4$$

Divide both sides by -16.

$$t^{2}=\frac{-4}{-16}$$

Reduce the fraction \frac{-4}{-16} to lowest terms by extracting and canceling out -4.

$$t^{2}=\frac{1}{4}$$

Take the square root of both sides of the equation.

$$t=\frac{1}{2} t=-\frac{1}{2}$$

Steps Using the Quadratic Formula

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

$$5-16t^{2}=1$$

Subtract 1 from both sides.

$$5-16t^{2}-1=0$$

Subtract 1 from 5 to get 4.

$$4-16t^{2}=0$$

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.

$$-16t^{2}+4=0$$

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

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

Square 0.

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

Multiply -4 times -16.

$$t=\frac{0±\sqrt{64\times 4}}{2\left(-16\right)}$$

Multiply 64 times 4.

$$t=\frac{0±\sqrt{256}}{2\left(-16\right)}$$

Take the square root of 256.

$$t=\frac{0±16}{2\left(-16\right)}$$

Multiply 2 times -16.

$$t=\frac{0±16}{-32}$$

Now solve the equation t=\frac{0±16}{-32} when ± is plus. Reduce the fraction \frac{16}{-32} to lowest terms by extracting and canceling out 16.

$$t=-\frac{1}{2}$$

Now solve the equation t=\frac{0±16}{-32} when ± is minus. Reduce the fraction \frac{-16}{-32} to lowest terms by extracting and canceling out 16.

$$t=\frac{1}{2}$$

The equation is now solved.

$$t=-\frac{1}{2} t=\frac{1}{2}$$