Write in Standard Form (-9- square root of -18)/3

$\frac{- 9 - \sqrt{- 18}}{3}$

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 $- 18$ as $- 1 (18)$ .

$\frac{- 9 - \sqrt{- 1 (18)}}{3}$

Rewrite $\sqrt{- 1 (18)}$ as $\sqrt{- 1} \cdot \sqrt{18}$ .

$\frac{- 9 - (\sqrt{- 1} \cdot \sqrt{18})}{3}$

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

$\frac{- 9 - (i \cdot \sqrt{18})}{3}$

Step 3

Simplify the numerator.

Rewrite $18$ as $3^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$\frac{- 9 - i \cdot \sqrt{9 (2)}}{3}$

Rewrite $9$ as $3^{2}$ .

$\frac{- 9 - i \cdot \sqrt{3^{2} \cdot 2}}{3}$

Pull terms out from under the radical.

$\frac{- 9 - i \cdot (3 \sqrt{2})}{3}$

Multiply $3$ by $- 1$ .

$\frac{- 9 - 3 i \sqrt{2}}{3}$

Step 4

Cancel the common factor of $- 9 - 3 i \sqrt{2}$ and $3$ .

Factor $3$ out of $- 9$ .

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

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

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

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

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

Cancel the common factors.

Factor $3$ out of $3$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{- 3 - i \sqrt{2}}{1}$

Divide $- 3 - i \sqrt{2}$ by $1$ .

$- 3 - i \sqrt{2}$