Trigonometry Examples

$\frac{- 8 + \sqrt{64 + 120}}{10}$

Step 1

Simplify the numerator.

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Step 1.1

Add $64$ and $120$ .

$\frac{- 8 + \sqrt{184}}{10}$

Step 1.2

Rewrite $184$ as $2^{2} \cdot 46$ .

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Step 1.2.1

Factor $4$ out of $184$ .

$\frac{- 8 + \sqrt{4 (46)}}{10}$

Step 1.2.2

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

$\frac{- 8 + \sqrt{2^{2} \cdot 46}}{10}$

$\frac{- 8 + \sqrt{2^{2} \cdot 46}}{10}$

Step 1.3

Pull terms out from under the radical.

$\frac{- 8 + 2 \sqrt{46}}{10}$

$\frac{- 8 + 2 \sqrt{46}}{10}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $- 8 + 2 \sqrt{46}$ and $10$ .

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Step 2.1.1

Factor $2$ out of $- 8$ .

$\frac{2 \cdot - 4 + 2 \sqrt{46}}{10}$

Step 2.1.2

Factor $2$ out of $2 \sqrt{46}$ .

$\frac{2 \cdot - 4 + 2 (\sqrt{46})}{10}$

Step 2.1.3

Factor $2$ out of $2 \cdot - 4 + 2 (\sqrt{46})$ .

$\frac{2 \cdot (- 4 + \sqrt{46})}{10}$

Step 2.1.4

Cancel the common factors.

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Step 2.1.4.1

Factor $2$ out of $10$ .

$\frac{2 \cdot (- 4 + \sqrt{46})}{2 (5)}$

Step 2.1.4.2

Cancel the common factor.

$\frac{2 \cdot (- 4 + \sqrt{46})}{2 \cdot 5}$

Step 2.1.4.3

Rewrite the expression.

$\frac{- 4 + \sqrt{46}}{5}$

$\frac{- 4 + \sqrt{46}}{5}$

$\frac{- 4 + \sqrt{46}}{5}$

Step 2.2

Rewrite $- 4$ as $- 1 (4)$ .

$\frac{- 1 (4) + \sqrt{46}}{5}$

Step 2.3

Factor $- 1$ out of $\sqrt{46}$ .

$\frac{- 1 (4) - 1 (- \sqrt{46})}{5}$

Step 2.4

Factor $- 1$ out of $- 1 (4) - 1 (- \sqrt{46})$ .

$\frac{- 1 (4 - \sqrt{46})}{5}$

Step 2.5

Move the negative in front of the fraction.

$- \frac{4 - \sqrt{46}}{5}$

$- \frac{4 - \sqrt{46}}{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- \frac{4 - \sqrt{46}}{5}$

Decimal Form:

$0.55646599 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$