Precalculus Examples

$93 = 201 t - 16 t^{2}$

Step 1

Rewrite the equation as $201 t - 16 t^{2} = 93$ .

$201 t - 16 t^{2} = 93$

Step 2

Subtract $93$ from both sides of the equation.

$201 t - 16 t^{2} - 93 = 0$

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 $a = - 16$ , $b = 201$ , and $c = - 93$ into the quadratic formula and solve for $t$ .

$\frac{- 201 \pm \sqrt{201^{2} - 4 \cdot (- 16 \cdot - 93)}}{2 \cdot - 16}$

Step 5

Simplify.

Tap for more steps...

Step 5.1

Simplify the numerator.

Tap for more steps...

Step 5.1.1

Raise $201$ to the power of $2$ .

$t = \frac{- 201 \pm \sqrt{40401 - 4 \cdot - 16 \cdot - 93}}{2 \cdot - 16}$

Step 5.1.2

Multiply $- 4 \cdot - 16 \cdot - 93$ .

Tap for more steps...

Step 5.1.2.1

Multiply $- 4$ by $- 16$ .

$t = \frac{- 201 \pm \sqrt{40401 + 64 \cdot - 93}}{2 \cdot - 16}$

Step 5.1.2.2

Multiply $64$ by $- 93$ .

$t = \frac{- 201 \pm \sqrt{40401 - 5952}}{2 \cdot - 16}$

Step 5.1.3

Subtract $5952$ from $40401$ .

$t = \frac{- 201 \pm \sqrt{34449}}{2 \cdot - 16}$

Step 5.2

Multiply $2$ by $- 16$ .

$t = \frac{- 201 \pm \sqrt{34449}}{- 32}$

Step 5.3

Simplify $\frac{- 201 \pm \sqrt{34449}}{- 32}$ .

$t = \frac{201 \pm \sqrt{34449}}{32}$

Step 6

The final answer is the combination of both solutions.

$t = \frac{201 + \sqrt{34449}}{32}, \frac{201 - \sqrt{34449}}{32}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$t = \frac{201 + \sqrt{34449}}{32}, \frac{201 - \sqrt{34449}}{32}$

Decimal Form:

$t = 12.08138806 \dots, 0.48111193 \dots$