Basic Math Examples

$2 - 7 \sqrt{- 18} + (- 3 + 4 \sqrt{- 50})$

Step 1

Remove parentheses.

$2 - 7 \sqrt{- 18} - 3 + 4 \sqrt{- 50}$

Step 2

Simplify each term.

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Step 2.1

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

$2 - 7 \sqrt{- 1 (18)} - 3 + 4 \sqrt{- 50}$

Step 2.2

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

$2 - 7 (\sqrt{- 1} \cdot \sqrt{18}) - 3 + 4 \sqrt{- 50}$

Step 2.3

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

$2 - 7 (i \cdot \sqrt{18}) - 3 + 4 \sqrt{- 50}$

Step 2.4

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

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Step 2.4.1

Factor $9$ out of $18$ .

$2 - 7 (i \cdot \sqrt{9 (2)}) - 3 + 4 \sqrt{- 50}$

Step 2.4.2

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

$2 - 7 (i \cdot \sqrt{3^{2} \cdot 2}) - 3 + 4 \sqrt{- 50}$

Step 2.5

Pull terms out from under the radical.

$2 - 7 (i \cdot (3 \sqrt{2})) - 3 + 4 \sqrt{- 50}$

Step 2.6

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

$2 - 7 (3 \cdot i \sqrt{2}) - 3 + 4 \sqrt{- 50}$

Step 2.7

Multiply $3$ by $- 7$ .

$2 - 21 (i \sqrt{2}) - 3 + 4 \sqrt{- 50}$

Step 2.8

Rewrite $- 50$ as $- 1 (50)$ .

$2 - 21 i \sqrt{2} - 3 + 4 \sqrt{- 1 (50)}$

Step 2.9

Rewrite $\sqrt{- 1 (50)}$ as $\sqrt{- 1} \cdot \sqrt{50}$ .

$2 - 21 i \sqrt{2} - 3 + 4 (\sqrt{- 1} \cdot \sqrt{50})$

Step 2.10

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

$2 - 21 i \sqrt{2} - 3 + 4 (i \cdot \sqrt{50})$

Step 2.11

Rewrite $50$ as $5^{2} \cdot 2$ .

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Step 2.11.1

Factor $25$ out of $50$ .

$2 - 21 i \sqrt{2} - 3 + 4 (i \cdot \sqrt{25 (2)})$

Step 2.11.2

Rewrite $25$ as $5^{2}$ .

$2 - 21 i \sqrt{2} - 3 + 4 (i \cdot \sqrt{5^{2} \cdot 2})$

Step 2.12

Pull terms out from under the radical.

$2 - 21 i \sqrt{2} - 3 + 4 (i \cdot (5 \sqrt{2}))$

Step 2.13

Move $5$ to the left of $i$ .

$2 - 21 i \sqrt{2} - 3 + 4 (5 \cdot i \sqrt{2})$

Step 2.14

Multiply $5$ by $4$ .

$2 - 21 i \sqrt{2} - 3 + 20 i \sqrt{2}$

Step 3

Simplify by adding terms.

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Step 3.1

Subtract $3$ from $2$ .

$- 21 i \sqrt{2} - 1 + 20 i \sqrt{2}$

Step 3.2

Add $- 21 i \sqrt{2}$ and $20 i \sqrt{2}$ .

$- i \sqrt{2} - 1$

Step 3.3

Reorder $- i \sqrt{2}$ and $- 1$ .

$- 1 - i \sqrt{2}$