Algebra Examples

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

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.

Tap for more steps...

Step 2.1

Subtract $1800$ from both sides of the equation.

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

Step 2.2

Subtract $1800$ from $1000$ .

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

Step 3

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

Tap for more steps...

Step 3.1

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

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

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Cancel the common factor of $- 16$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor.

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

Step 3.2.1.2

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

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

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Divide $- 800$ by $- 16$ .

$t^{2} = 50$

Step 4

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

$t = \pm \sqrt{50}$

Step 5

Simplify $\pm \sqrt{50}$ .

Tap for more steps...

Step 5.1

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

Tap for more steps...

Step 5.1.1

Factor $25$ out of $50$ .

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

Step 5.1.2

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

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

Step 5.2

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.

Tap for more steps...

Step 6.1

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

$t = 5 \sqrt{2}$

Step 6.2

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

$t = - 5 \sqrt{2}$

Step 6.3

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:

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