Precalculus Examples

$0 = - 16 t^{2} + 100$

Step 1

Rewrite the equation as $- 16 t^{2} + 100 = 0$ .

$- 16 t^{2} + 100 = 0$

Step 2

Subtract $100$ from both sides of the equation.

$- 16 t^{2} = - 100$

Step 3

Divide each term in $- 16 t^{2} = - 100$ by $- 16$ and simplify.

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Step 3.1

Divide each term in $- 16 t^{2} = - 100$ by $- 16$ .

$\frac{- 16 t^{2}}{- 16} = \frac{- 100}{- 16}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 16$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 16 t^{2}}{- 16} = \frac{- 100}{- 16}$

Step 3.2.1.2

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

$t^{2} = \frac{- 100}{- 16}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Cancel the common factor of $- 100$ and $- 16$ .

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Step 3.3.1.1

Factor $- 4$ out of $- 100$ .

$t^{2} = \frac{- 4 (25)}{- 16}$

Step 3.3.1.2

Cancel the common factors.

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Step 3.3.1.2.1

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

$t^{2} = \frac{- 4 \cdot 25}{- 4 \cdot 4}$

Step 3.3.1.2.2

Cancel the common factor.

$t^{2} = \frac{- 4 \cdot 25}{- 4 \cdot 4}$

Step 3.3.1.2.3

Rewrite the expression.

$t^{2} = \frac{25}{4}$

Step 4

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

$t = \pm \sqrt{\frac{25}{4}}$

Step 5

Simplify $\pm \sqrt{\frac{25}{4}}$ .

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Step 5.1

Rewrite $\sqrt{\frac{25}{4}}$ as $\frac{\sqrt{25}}{\sqrt{4}}$ .

$t = \pm \frac{\sqrt{25}}{\sqrt{4}}$

Step 5.2

Simplify the numerator.

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Step 5.2.1

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

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

Step 5.2.2

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

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

Step 5.3

Simplify the denominator.

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Step 5.3.1

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

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

Step 5.3.2

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

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

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.

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

Step 6.2

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

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

Step 6.3

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

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

Step 7

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$t = 2.5, - 2.5$

Mixed Number Form:

$t = 2 \frac{1}{2}, - 2 \frac{1}{2}$