Trigonometry Examples

$\frac{- 6 - \sqrt{6^{2} - 4 \cdot 1 \cdot 2}}{2 (1)}$

Step 1

Simplify the numerator.

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Step 1.1

Raise $6$ to the power of $2$ .

$\frac{- 6 - \sqrt{36 - 4 \cdot 1 \cdot 2}}{2 (1)}$

Step 1.2

Multiply $- 4 \cdot 1 \cdot 2$ .

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Step 1.2.1

Multiply $- 4$ by $1$ .

$\frac{- 6 - \sqrt{36 - 4 \cdot 2}}{2 (1)}$

Step 1.2.2

Multiply $- 4$ by $2$ .

$\frac{- 6 - \sqrt{36 - 8}}{2 (1)}$

Step 1.3

Subtract $8$ from $36$ .

$\frac{- 6 - \sqrt{28}}{2 (1)}$

Step 1.4

Rewrite $28$ as $2^{2} \cdot 7$ .

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Step 1.4.1

Factor $4$ out of $28$ .

$\frac{- 6 - \sqrt{4 (7)}}{2 (1)}$

Step 1.4.2

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

$\frac{- 6 - \sqrt{2^{2} \cdot 7}}{2 (1)}$

Step 1.5

Pull terms out from under the radical.

$\frac{- 6 - (2 \sqrt{7})}{2 (1)}$

Step 1.6

Multiply $2$ by $- 1$ .

$\frac{- 6 - 2 \sqrt{7}}{2 (1)}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Multiply $2$ by $1$ .

$\frac{- 6 - 2 \sqrt{7}}{2}$

Step 2.2

Cancel the common factor of $- 6 - 2 \sqrt{7}$ and $2$ .

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Step 2.2.1

Factor $2$ out of $- 6$ .

$\frac{2 \cdot - 3 - 2 \sqrt{7}}{2}$

Step 2.2.2

Factor $2$ out of $- 2 \sqrt{7}$ .

$\frac{2 \cdot - 3 + 2 (- \sqrt{7})}{2}$

Step 2.2.3

Factor $2$ out of $2 (- 3) + 2 (- \sqrt{7})$ .

$\frac{2 (- 3 - \sqrt{7})}{2}$

Step 2.2.4

Cancel the common factors.

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Step 2.2.4.1

Factor $2$ out of $2$ .

$\frac{2 (- 3 - \sqrt{7})}{2 (1)}$

Step 2.2.4.2

Cancel the common factor.

$\frac{2 (- 3 - \sqrt{7})}{2 \cdot 1}$

Step 2.2.4.3

Rewrite the expression.

$\frac{- 3 - \sqrt{7}}{1}$

Step 2.2.4.4

Divide $- 3 - \sqrt{7}$ by $1$ .

$- 3 - \sqrt{7}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 3 - \sqrt{7}$

Decimal Form:

$- 5.64575131 \dots$