Trigonometry Examples

$- \frac{12 (\sqrt{- 12^{2} - 4 \cdot 2 \cdot 10})}{2 (2)}$

Step 1

Cancel the common factor of $12$ and $2$ .

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Step 1.1

Factor $2$ out of $12 (\sqrt{- 12^{2} - 4 \cdot 2 \cdot 10})$ .

$- \frac{2 (6 \sqrt{- 12^{2} - 4 \cdot 2 \cdot 10})}{2 (2)}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Cancel the common factor.

$- \frac{2 (6 \sqrt{- 12^{2} - 4 \cdot 2 \cdot 10})}{2 \cdot 2}$

Step 1.2.2

Rewrite the expression.

$- \frac{6 \sqrt{- 12^{2} - 4 \cdot 2 \cdot 10}}{2}$

Step 2

Cancel the common factor of $6$ and $2$ .

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Step 2.1

Factor $2$ out of $6 \sqrt{- 12^{2} - 4 \cdot 2 \cdot 10}$ .

$- \frac{2 (3 \sqrt{- 12^{2} - 4 \cdot 2 \cdot 10})}{2}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $2$ out of $2$ .

$- \frac{2 (3 \sqrt{- 12^{2} - 4 \cdot 2 \cdot 10})}{2 (1)}$

Step 2.2.2

Cancel the common factor.

$- \frac{2 (3 \sqrt{- 12^{2} - 4 \cdot 2 \cdot 10})}{2 \cdot 1}$

Step 2.2.3

Rewrite the expression.

$- \frac{3 \sqrt{- 12^{2} - 4 \cdot 2 \cdot 10}}{1}$

Step 2.2.4

Divide $3 \sqrt{- 12^{2} - 4 \cdot 2 \cdot 10}$ by $1$ .

$- (3 \sqrt{- 12^{2} - 4 \cdot 2 \cdot 10})$

Step 3

Simplify the expression.

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Step 3.1

Raise $12$ to the power of $2$ .

$- (3 \sqrt{- 1 \cdot 144 - 4 \cdot 2 \cdot 10})$

Step 3.2

Multiply $- 1$ by $144$ .

$- (3 \sqrt{- 144 - 4 \cdot 2 \cdot 10})$

Step 4

Multiply $- 4 \cdot 2 \cdot 10$ .

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Step 4.1

Multiply $- 4$ by $2$ .

$- (3 \sqrt{- 144 - 8 \cdot 10})$

Step 4.2

Multiply $- 8$ by $10$ .

$- (3 \sqrt{- 144 - 80})$

Step 5

Subtract $80$ from $- 144$ .

$- (3 \sqrt{- 224})$

Step 6

Rewrite $- 224$ as $- 1 (224)$ .

$- (3 \sqrt{- 1 (224)})$

Step 7

Rewrite $\sqrt{- 1 (224)}$ as $\sqrt{- 1} \cdot \sqrt{224}$ .

$- (3 (\sqrt{- 1} \cdot \sqrt{224}))$

Step 8

Rewrite $\sqrt{- 1}$ as $i$ .

$- (3 (i \cdot \sqrt{224}))$

Step 9

Rewrite $224$ as $4^{2} \cdot 14$ .

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Step 9.1

Factor $16$ out of $224$ .

$- (3 (i \cdot \sqrt{16 (14)}))$

Step 9.2

Rewrite $16$ as $4^{2}$ .

$- (3 (i \cdot \sqrt{4^{2} \cdot 14}))$

Step 10

Pull terms out from under the radical.

$- (3 (i \cdot (4 \sqrt{14})))$

Step 11

Simplify the expression.

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Step 11.1

Move $4$ to the left of $i$ .

$- (3 (4 \cdot i \sqrt{14}))$

Step 11.2

Multiply $4$ by $3$ .

$- (12 (i \sqrt{14}))$

Step 11.3

Multiply $12$ by $- 1$ .

$- 12 i \sqrt{14}$