Finite Math Examples

$9 = - 16 t^{2} + 8 + 33$

Step 1

Rewrite the equation as $- 16 t^{2} + 8 + 33 = 9$ .

$- 16 t^{2} + 8 + 33 = 9$

Step 2

Add $8$ and $33$ .

$- 16 t^{2} + 41 = 9$

Step 3

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

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Step 3.1

Subtract $41$ from both sides of the equation.

$- 16 t^{2} = 9 - 41$

Step 3.2

Subtract $41$ from $9$ .

$- 16 t^{2} = - 32$

Step 4

Divide each term in $- 16 t^{2} = - 32$ by $- 16$ and simplify.

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Step 4.1

Divide each term in $- 16 t^{2} = - 32$ by $- 16$ .

$\frac{- 16 t^{2}}{- 16} = \frac{- 32}{- 16}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 16$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 16 t^{2}}{- 16} = \frac{- 32}{- 16}$

Step 4.2.1.2

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

$t^{2} = \frac{- 32}{- 16}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 32$ by $- 16$ .

$t^{2} = 2$

Step 5

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

$t = \pm \sqrt{2}$

Step 6

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

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Step 6.1

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

$t = \sqrt{2}$

Step 6.2

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

$t = - \sqrt{2}$

Step 6.3

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

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

Step 7

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$t = 1.41421356 \dots, - 1.41421356 \dots$