Algebra Examples

$f (x) = 2 \sqrt{- 9}$

Step 1

Simplify $2 \sqrt{- 9}$ .

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Step 1.1

Rewrite.

$f (x) = 0 + 0 + 2 \sqrt{- 9}$

Step 1.2

Simplify by adding zeros.

$f (x) = 2 \sqrt{- 9}$

Step 1.3

Rewrite $- 9$ as $- 1 (9)$ .

$f (x) = 2 \sqrt{- 1 (9)}$

Step 1.4

Rewrite $\sqrt{- 1 (9)}$ as $\sqrt{- 1} \cdot \sqrt{9}$ .

$f (x) = 2 (\sqrt{- 1} \cdot \sqrt{9})$

Step 1.5

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

$f (x) = 2 (i \cdot \sqrt{9})$

Step 1.6

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

$f (x) = 2 (i \cdot \sqrt{3^{2}})$

Step 1.7

Pull terms out from under the radical, assuming positive real numbers.

$f (x) = 2 (i \cdot 3)$

Step 1.8

Move $3$ to the left of $i$ .

$f (x) = 2 (3 \cdot i)$

Step 1.9

Multiply $3$ by $2$ .

$f (x) = 6 i$

Step 2

Move all terms not containing $f$ to the right side of the equation.

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Step 2.1

Subtract $f (x)$ from both sides of the equation.

$0 = 6 i - f (x)$

Step 2.2

Reorder $6 i$ and $- f (x)$ .

$0 = - f (x) + 6 i$

Step 3

Rewrite the equation as $- f (x) + 6 i = 0$ .

$- f (x) + 6 i = 0$