Write in Standard Form (-6- square root of -12)/48

$\frac{- 6 - \sqrt{- 12}}{48}$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Pull out imaginary unit $i$ .

Rewrite $- 12$ as $- 1 (12)$ .

$\frac{- 6 - \sqrt{- 1 (12)}}{48}$

Rewrite $\sqrt{- 1 (12)}$ as $\sqrt{- 1} \cdot \sqrt{12}$ .

$\frac{- 6 - (\sqrt{- 1} \cdot \sqrt{12})}{48}$

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

$\frac{- 6 - (i \cdot \sqrt{12})}{48}$

Step 3

Simplify the numerator.

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$\frac{- 6 - i \cdot \sqrt{4 (3)}}{48}$

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

$\frac{- 6 - i \cdot \sqrt{2^{2} \cdot 3}}{48}$

Pull terms out from under the radical.

$\frac{- 6 - i \cdot (2 \sqrt{3})}{48}$

Multiply $2$ by $- 1$ .

$\frac{- 6 - 2 i \sqrt{3}}{48}$

Step 4

Simplify terms.

Cancel the common factor of $- 6 - 2 i \sqrt{3}$ and $48$ .

Factor $2$ out of $- 6$ .

$\frac{2 (- 3) - 2 i \sqrt{3}}{48}$

Factor $2$ out of $- 2 i \sqrt{3}$ .

$\frac{2 (- 3) + 2 (- i \sqrt{3})}{48}$

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

$\frac{2 (- 3 - i \sqrt{3})}{48}$

Cancel the common factors.

Factor $2$ out of $48$ .

$\frac{2 (- 3 - i \sqrt{3})}{2 \cdot 24}$

Cancel the common factor.

$\frac{2 (- 3 - i \sqrt{3})}{2 \cdot 24}$

Rewrite the expression.

$\frac{- 3 - i \sqrt{3}}{24}$

Rewrite $- 3$ as $- 1 (3)$ .

$\frac{- 1 (3) - i \sqrt{3}}{24}$

Factor $- 1$ out of $- i \sqrt{3}$ .

$\frac{- 1 (3) - (i \sqrt{3})}{24}$

Factor $- 1$ out of $- 1 (3) - (i \sqrt{3})$ .

$\frac{- 1 (3 + i \sqrt{3})}{24}$

Move the negative in front of the fraction.

$- \frac{3 + i \sqrt{3}}{24}$

Write in Standard Form (-6- square root of -12)/48

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