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

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

Step 1

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

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

Step 2

Subtract $64$ from both sides of the equation.

$- 16 t^{2} = h - 64$

Step 3

Divide each term in $- 16 t^{2} = h - 64$ by $- 16$ and simplify.

Divide each term in $- 16 t^{2} = h - 64$ by $- 16$ .

$\frac{- 16 t^{2}}{- 16} = \frac{h}{- 16} + \frac{- 64}{- 16}$

Simplify the left side.

Cancel the common factor of $- 16$ .

Cancel the common factor.

$\frac{- 16 t^{2}}{- 16} = \frac{h}{- 16} + \frac{- 64}{- 16}$

Divide $t^{2}$ by $1$ .

$t^{2} = \frac{h}{- 16} + \frac{- 64}{- 16}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$t^{2} = - \frac{h}{16} + \frac{- 64}{- 16}$

Divide $- 64$ by $- 16$ .

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

Step 4

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$t = \pm \sqrt{- \frac{h}{16} + 4}$

Step 5

Simplify $\pm \sqrt{- \frac{h}{16} + 4}$ .

To write $4$ as a fraction with a common denominator, multiply by $\frac{16}{16}$ .

$t = \pm \sqrt{- \frac{h}{16} + 4 \cdot \frac{16}{16}}$

Combine $4$ and $\frac{16}{16}$ .

$t = \pm \sqrt{- \frac{h}{16} + \frac{4 \cdot 16}{16}}$

Combine the numerators over the common denominator.

$t = \pm \sqrt{\frac{- h + 4 \cdot 16}{16}}$

Multiply $4$ by $16$ .

$t = \pm \sqrt{\frac{- h + 64}{16}}$

Rewrite $\frac{- h + 64}{16}$ as ${(\frac{1}{4})}^{2} (- h + 64)$ .

Factor the perfect power $1^{2}$ out of $- h + 64$ .

$t = \pm \sqrt{\frac{1^{2} (- h + 64)}{16}}$

Factor the perfect power $4^{2}$ out of $16$ .

$t = \pm \sqrt{\frac{1^{2} (- h + 64)}{4^{2} \cdot 1}}$

Rearrange the fraction $\frac{1^{2} (- h + 64)}{4^{2} \cdot 1}$ .

$t = \pm \sqrt{{(\frac{1}{4})}^{2} (- h + 64)}$

Pull terms out from under the radical.

$t = \pm \frac{1}{4} \sqrt{- h + 64}$

Combine $\frac{1}{4}$ and $\sqrt{- h + 64}$ .

$t = \pm \frac{\sqrt{- h + 64}}{4}$

Step 6

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

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

Next, use the negative value of the $\pm$ to find the second solution.

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

The complete solution is the result of both the positive and negative portions of the solution.

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

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

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

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

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

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