Algebra Examples

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

Step 1

Pull out imaginary unit $i$ .

Tap for more steps...

Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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

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

Step 2

Simplify the numerator.

Tap for more steps...

Step 2.1

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

Tap for more steps...

Step 2.1.1

Factor $9$ out of $18$ .

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

Step 2.1.2

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

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

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

Step 2.2

Pull terms out from under the radical.

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

Step 2.3

Multiply $3$ by $- 1$ .

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

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

Step 3

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

Tap for more steps...

Step 3.1

Factor $3$ out of $- 9$ .

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

Step 3.2

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

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

Step 3.3

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

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

Step 3.4

Cancel the common factors.

Tap for more steps...

Step 3.4.1

Factor $3$ out of $3$ .

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

Step 3.4.2

Cancel the common factor.

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

Step 3.4.3

Rewrite the expression.

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

Step 3.4.4

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

$- 3 - i \sqrt{2}$

$- 3 - i \sqrt{2}$

$- 3 - i \sqrt{2}$

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