Solve for t s=-16t^2+64t

$s = - 16 t^{2} + 64 t$

Step 1

Rewrite the equation as $- 16 t^{2} + 64 t = s$ .

$- 16 t^{2} + 64 t = s$

Step 2

Subtract $s$ from both sides of the equation.

$- 16 t^{2} + 64 t - s = 0$

Step 3

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 4

Substitute the values $a = - 16$ , $b = 64$ , and $c = - s$ into the quadratic formula and solve for $t$ .

$\frac{- 64 \pm \sqrt{64^{2} - 4 \cdot (- 16 \cdot (- s))}}{2 \cdot - 16}$

Step 5

Simplify.

Simplify the numerator.

Raise $64$ to the power of $2$ .

$t = \frac{- 64 \pm \sqrt{4096 - 4 \cdot - 16 \cdot (- 1 s)}}{2 \cdot - 16}$

Multiply $- 4 \cdot - 16 \cdot - 1$ .

Multiply $- 4$ by $- 16$ .

$t = \frac{- 64 \pm \sqrt{4096 + 64 \cdot (- 1 s)}}{2 \cdot - 16}$

Multiply $64$ by $- 1$ .

$t = \frac{- 64 \pm \sqrt{4096 - 64 s}}{2 \cdot - 16}$

Factor $64$ out of $4096 - 64 s$ .

Factor $64$ out of $4096$ .

$t = \frac{- 64 \pm \sqrt{64 (64) - 64 s}}{2 \cdot - 16}$

Factor $64$ out of $- 64 s$ .

$t = \frac{- 64 \pm \sqrt{64 (64) + 64 (- s)}}{2 \cdot - 16}$

Factor $64$ out of $64 (64) + 64 (- s)$ .

$t = \frac{- 64 \pm \sqrt{64 (64 - s)}}{2 \cdot - 16}$

Rewrite $64 (64 - s)$ as $8^{2} (8^{2} - s)$ .

Rewrite $64$ as $8^{2}$ .

$t = \frac{- 64 \pm \sqrt{8^{2} (64 - s)}}{2 \cdot - 16}$

Rewrite $64$ as $8^{2}$ .

$t = \frac{- 64 \pm \sqrt{8^{2} (8^{2} - s)}}{2 \cdot - 16}$

Pull terms out from under the radical.

$t = \frac{- 64 \pm 8 \sqrt{8^{2} - s}}{2 \cdot - 16}$

Raise $8$ to the power of $2$ .

$t = \frac{- 64 \pm 8 \sqrt{64 - s}}{2 \cdot - 16}$

Multiply $2$ by $- 16$ .

$t = \frac{- 64 \pm 8 \sqrt{64 - s}}{- 32}$

Simplify $\frac{- 64 \pm 8 \sqrt{64 - s}}{- 32}$ .

$t = \frac{8 \pm \sqrt{64 - s}}{4}$

Step 6

The final answer is the combination of both solutions.

$t = \frac{8 + \sqrt{64 - s}}{4}$

$t = \frac{8 - \sqrt{64 - s}}{4}$

Solve for t s=-16t^2+64t

Related Questions

Support LCMGCF.com by disabling your adblocker.