Solve for t h=-16t^2+1156

$h = - 16 t^{2} + 1156$

Step 1

Rewrite the equation as $- 16 t^{2} + 1156 = h$ .

$- 16 t^{2} + 1156 = h$

Step 2

Subtract $1156$ from both sides of the equation.

$- 16 t^{2} = h - 1156$

Step 3

Divide each term in $- 16 t^{2} = h - 1156$ by $- 16$ and simplify.

Divide each term in $- 16 t^{2} = h - 1156$ by $- 16$ .

$\frac{- 16 t^{2}}{- 16} = \frac{h}{- 16} + \frac{- 1156}{- 16}$

Simplify the left side.

Cancel the common factor of $- 16$ .

Cancel the common factor.

$\frac{- 16 t^{2}}{- 16} = \frac{h}{- 16} + \frac{- 1156}{- 16}$

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

$t^{2} = \frac{h}{- 16} + \frac{- 1156}{- 16}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$t^{2} = - \frac{h}{16} + \frac{- 1156}{- 16}$

Cancel the common factor of $- 1156$ and $- 16$ .

Factor $- 4$ out of $- 1156$ .

$t^{2} = - \frac{h}{16} + \frac{- 4 (289)}{- 16}$

Cancel the common factors.

Factor $- 4$ out of $- 16$ .

$t^{2} = - \frac{h}{16} + \frac{- 4 \cdot 289}{- 4 \cdot 4}$

Cancel the common factor.

$t^{2} = - \frac{h}{16} + \frac{- 4 \cdot 289}{- 4 \cdot 4}$

Rewrite the expression.

$t^{2} = - \frac{h}{16} + \frac{289}{4}$

Step 4

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

$t = \pm \sqrt{- \frac{h}{16} + \frac{289}{4}}$

Step 5

Simplify $\pm \sqrt{- \frac{h}{16} + \frac{289}{4}}$ .

To write $\frac{289}{4}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$t = \pm \sqrt{- \frac{h}{16} + \frac{289}{4} \cdot \frac{4}{4}}$

Write each expression with a common denominator of $16$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{289}{4}$ by $\frac{4}{4}$ .

$t = \pm \sqrt{- \frac{h}{16} + \frac{289 \cdot 4}{4 \cdot 4}}$

Multiply $4$ by $4$ .

$t = \pm \sqrt{- \frac{h}{16} + \frac{289 \cdot 4}{16}}$

Combine the numerators over the common denominator.

$t = \pm \sqrt{\frac{- h + 289 \cdot 4}{16}}$

Multiply $289$ by $4$ .

$t = \pm \sqrt{\frac{- h + 1156}{16}}$

Rewrite $\frac{- h + 1156}{16}$ as ${(\frac{1}{4})}^{2} (- h + 1156)$ .

Factor the perfect power $1^{2}$ out of $- h + 1156$ .

$t = \pm \sqrt{\frac{1^{2} (- h + 1156)}{16}}$

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

$t = \pm \sqrt{\frac{1^{2} (- h + 1156)}{4^{2} \cdot 1}}$

Rearrange the fraction $\frac{1^{2} (- h + 1156)}{4^{2} \cdot 1}$ .

$t = \pm \sqrt{{(\frac{1}{4})}^{2} (- h + 1156)}$

Pull terms out from under the radical.

$t = \pm \frac{1}{4} \sqrt{- h + 1156}$

Combine $\frac{1}{4}$ and $\sqrt{- h + 1156}$ .

$t = \pm \frac{\sqrt{- h + 1156}}{4}$

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.

$t = \frac{\sqrt{- h + 1156}}{4}$

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

$t = - \frac{\sqrt{- h + 1156}}{4}$

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

$t = \frac{\sqrt{- h + 1156}}{4}$

$t = - \frac{\sqrt{- h + 1156}}{4}$

$t = \frac{\sqrt{- h + 1156}}{4}$

$t = - \frac{\sqrt{- h + 1156}}{4}$

Solve for t h=-16t^2+1156

Related Questions

Support LCMGCF.com by disabling your adblocker.