Trigonometry Examples

$h = - 25 t^{2} + c t + d$

Step 1

Rewrite the equation as $- 25 t^{2} + c t + d = h$ .

$- 25 t^{2} + c t + d = h$

Step 2

Subtract $h$ from both sides of the equation.

$- 25 t^{2} + c t + d - h = 0$

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 $a = - 25$ , $b = c$ , and $c = d - h$ into the quadratic formula and solve for $t$ .

$\frac{- c \pm \sqrt{c^{2} - 4 \cdot (- 25 \cdot (d - h))}}{2 \cdot - 25}$

Step 5

Simplify.

Tap for more steps...

Step 5.1

Simplify the numerator.

Tap for more steps...

Step 5.1.1

Multiply $- 4$ by $- 25$ .

$t = \frac{- c \pm \sqrt{c^{2} + 100 \cdot (d - h)}}{2 \cdot - 25}$

Step 5.1.2

Apply the distributive property.

$t = \frac{- c \pm \sqrt{c^{2} + 100 d + 100 (- h)}}{2 \cdot - 25}$

Step 5.1.3

Multiply $- 1$ by $100$ .

$t = \frac{- c \pm \sqrt{c^{2} + 100 d - 100 h}}{2 \cdot - 25}$

Step 5.2

Multiply $2$ by $- 25$ .

$t = \frac{- c \pm \sqrt{c^{2} + 100 d - 100 h}}{- 50}$

Step 5.3

Simplify $\frac{- c \pm \sqrt{c^{2} + 100 d - 100 h}}{- 50}$ .

$t = \frac{c \pm \sqrt{c^{2} + 100 d - 100 h}}{50}$

Step 6

The final answer is the combination of both solutions.

$t = \frac{c + \sqrt{c^{2} + 100 d - 100 h}}{50}$

$t = \frac{c - \sqrt{c^{2} + 100 d - 100 h}}{50}$