Solve for t 1000=-16t^2+1700

$1000 = - 16 t^{2} + 1700$

Step 1

Rewrite the equation as $- 16 t^{2} + 1700 = 1000$ .

$- 16 t^{2} + 1700 = 1000$

Step 2

Move all terms not containing $t$ to the right side of the equation.

Subtract $1700$ from both sides of the equation.

$- 16 t^{2} = 1000 - 1700$

Subtract $1700$ from $1000$ .

$- 16 t^{2} = - 700$

Step 3

Divide each term in $- 16 t^{2} = - 700$ by $- 16$ and simplify.

Divide each term in $- 16 t^{2} = - 700$ by $- 16$ .

$\frac{- 16 t^{2}}{- 16} = \frac{- 700}{- 16}$

Simplify the left side.

Cancel the common factor of $- 16$ .

Cancel the common factor.

$\frac{- 16 t^{2}}{- 16} = \frac{- 700}{- 16}$

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

$t^{2} = \frac{- 700}{- 16}$

Simplify the right side.

Cancel the common factor of $- 700$ and $- 16$ .

Factor $- 4$ out of $- 700$ .

$t^{2} = \frac{- 4 (175)}{- 16}$

Cancel the common factors.

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

$t^{2} = \frac{- 4 \cdot 175}{- 4 \cdot 4}$

Cancel the common factor.

$t^{2} = \frac{- 4 \cdot 175}{- 4 \cdot 4}$

Rewrite the expression.

$t^{2} = \frac{175}{4}$

Step 4

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

$t = \pm \sqrt{\frac{175}{4}}$

Step 5

Simplify $\pm \sqrt{\frac{175}{4}}$ .

Rewrite $\sqrt{\frac{175}{4}}$ as $\frac{\sqrt{175}}{\sqrt{4}}$ .

$t = \pm \frac{\sqrt{175}}{\sqrt{4}}$

Simplify the numerator.

Rewrite $175$ as $5^{2} \cdot 7$ .

Factor $25$ out of $175$ .

$t = \pm \frac{\sqrt{25 (7)}}{\sqrt{4}}$

Rewrite $25$ as $5^{2}$ .

$t = \pm \frac{\sqrt{5^{2} \cdot 7}}{\sqrt{4}}$

Pull terms out from under the radical.

$t = \pm \frac{5 \sqrt{7}}{\sqrt{4}}$

Simplify the denominator.

Rewrite $4$ as $2^{2}$ .

$t = \pm \frac{5 \sqrt{7}}{\sqrt{2^{2}}}$

Pull terms out from under the radical, assuming positive real numbers.

$t = \pm \frac{5 \sqrt{7}}{2}$

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.

$t = \frac{5 \sqrt{7}}{2}$

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

$t = - \frac{5 \sqrt{7}}{2}$

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

$t = \frac{5 \sqrt{7}}{2}, - \frac{5 \sqrt{7}}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$t = \frac{5 \sqrt{7}}{2}, - \frac{5 \sqrt{7}}{2}$

Decimal Form:

$t = 6.61437827 \dots, - 6.61437827 \dots$

Solve for t 1000=-16t^2+1700

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