Solve for t 1000=-16t^2+1800

$1000 = - 16 t^{2} + 1800$

Step 1

Rewrite the equation as $- 16 t^{2} + 1800 = 1000$ .

$- 16 t^{2} + 1800 = 1000$

Step 2

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

Subtract $1800$ from both sides of the equation.

$- 16 t^{2} = 1000 - 1800$

Subtract $1800$ from $1000$ .

$- 16 t^{2} = - 800$

Step 3

Divide each term in $- 16 t^{2} = - 800$ by $- 16$ and simplify.

Divide each term in $- 16 t^{2} = - 800$ by $- 16$ .

$\frac{- 16 t^{2}}{- 16} = \frac{- 800}{- 16}$

Simplify the left side.

Cancel the common factor of $- 16$ .

Cancel the common factor.

$\frac{- 16 t^{2}}{- 16} = \frac{- 800}{- 16}$

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

$t^{2} = \frac{- 800}{- 16}$

Simplify the right side.

Divide $- 800$ by $- 16$ .

$t^{2} = 50$

Step 4

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

$t = \pm \sqrt{50}$

Step 5

Simplify $\pm \sqrt{50}$ .

Rewrite $50$ as $5^{2} \cdot 2$ .

Factor $25$ out of $50$ .

$t = \pm \sqrt{25 (2)}$

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

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

Pull terms out from under the radical.

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

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.

$t = 5 \sqrt{2}$

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

$t = - 5 \sqrt{2}$

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

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

Step 7

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$t = 7.07106781 \dots, - 7.07106781 \dots$

Solve for t 1000=-16t^2+1800

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