Finite Math Examples

$t = - \frac{- 150 + \sqrt{23780}}{- 32}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $23780$ as $2^{2} \cdot 5945$ .

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Step 1.1.1

Factor $4$ out of $23780$ .

$t = - \frac{- 150 + \sqrt{4 (5945)}}{- 32}$

Step 1.1.2

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

$t = - \frac{- 150 + \sqrt{2^{2} \cdot 5945}}{- 32}$

Step 1.2

Pull terms out from under the radical.

$t = - \frac{- 150 + 2 \sqrt{5945}}{- 32}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $- 150 + 2 \sqrt{5945}$ and $- 32$ .

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Step 2.1.1

Factor $2$ out of $- 150$ .

$t = - \frac{2 \cdot - 75 + 2 \sqrt{5945}}{- 32}$

Step 2.1.2

Factor $2$ out of $2 \sqrt{5945}$ .

$t = - \frac{2 \cdot - 75 + 2 (\sqrt{5945})}{- 32}$

Step 2.1.3

Factor $2$ out of $2 \cdot - 75 + 2 (\sqrt{5945})$ .

$t = - \frac{2 \cdot (- 75 + \sqrt{5945})}{- 32}$

Step 2.1.4

Cancel the common factors.

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Step 2.1.4.1

Factor $2$ out of $- 32$ .

$t = - \frac{2 \cdot (- 75 + \sqrt{5945})}{2 (- 16)}$

Step 2.1.4.2

Cancel the common factor.

$t = - \frac{2 \cdot (- 75 + \sqrt{5945})}{2 \cdot - 16}$

Step 2.1.4.3

Rewrite the expression.

$t = - \frac{- 75 + \sqrt{5945}}{- 16}$

Step 2.2

Move the negative in front of the fraction.

$t = - - \frac{- 75 + \sqrt{5945}}{16}$

Step 3

Multiply $- - \frac{- 75 + \sqrt{5945}}{16}$ .

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Step 3.1

Multiply $- 1$ by $- 1$ .

$t = 1 \frac{- 75 + \sqrt{5945}}{16}$

Step 3.2

Multiply $\frac{- 75 + \sqrt{5945}}{16}$ by $1$ .

$t = \frac{- 75 + \sqrt{5945}}{16}$

Step 4

Rewrite $- 75$ as $- 1 (75)$ .

$t = \frac{- 1 (75) + \sqrt{5945}}{16}$

Step 5

Factor $- 1$ out of $\sqrt{5945}$ .

$t = \frac{- 1 (75) - 1 (- \sqrt{5945})}{16}$

Step 6

Factor $- 1$ out of $- 1 (75) - 1 (- \sqrt{5945})$ .

$t = \frac{- 1 (75 - \sqrt{5945})}{16}$

Step 7

Move the negative in front of the fraction.

$t = - \frac{75 - \sqrt{5945}}{16}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$t = - \frac{75 - \sqrt{5945}}{16}$

Decimal Form:

$t = 0.13148913 \dots$