Basic Math Examples

$\frac{6 + \sqrt{- 6^{2} - 4 \cdot 1 \cdot 6}}{2}$

Step 1

Simplify the numerator.

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Step 1.1

Raise $6$ to the power of $2$ .

$\frac{6 + \sqrt{- 1 \cdot 36 - 4 \cdot 1 \cdot 6}}{2}$

Step 1.2

Multiply $- 1$ by $36$ .

$\frac{6 + \sqrt{- 36 - 4 \cdot 1 \cdot 6}}{2}$

Step 1.3

Multiply $- 4 \cdot 1 \cdot 6$ .

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Step 1.3.1

Multiply $- 4$ by $1$ .

$\frac{6 + \sqrt{- 36 - 4 \cdot 6}}{2}$

Step 1.3.2

Multiply $- 4$ by $6$ .

$\frac{6 + \sqrt{- 36 - 24}}{2}$

Step 1.4

Subtract $24$ from $- 36$ .

$\frac{6 + \sqrt{- 60}}{2}$

Step 1.5

Rewrite $- 60$ as $- 1 (60)$ .

$\frac{6 + \sqrt{- 1 (60)}}{2}$

Step 1.6

Rewrite $\sqrt{- 1 (60)}$ as $\sqrt{- 1} \cdot \sqrt{60}$ .

$\frac{6 + \sqrt{- 1} \cdot \sqrt{60}}{2}$

Step 1.7

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

$\frac{6 + i \cdot \sqrt{60}}{2}$

Step 1.8

Rewrite $60$ as $2^{2} \cdot 15$ .

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Step 1.8.1

Factor $4$ out of $60$ .

$\frac{6 + i \cdot \sqrt{4 (15)}}{2}$

Step 1.8.2

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

$\frac{6 + i \cdot \sqrt{2^{2} \cdot 15}}{2}$

Step 1.9

Pull terms out from under the radical.

$\frac{6 + i \cdot (2 \sqrt{15})}{2}$

Step 1.10

Move $2$ to the left of $i$ .

$\frac{6 + 2 i \sqrt{15}}{2}$

Step 2

Cancel the common factor of $6 + 2 i \sqrt{15}$ and $2$ .

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Step 2.1

Factor $2$ out of $6$ .

$\frac{2 \cdot 3 + 2 i \sqrt{15}}{2}$

Step 2.2

Factor $2$ out of $2 i \sqrt{15}$ .

$\frac{2 \cdot 3 + 2 (i \sqrt{15})}{2}$

Step 2.3

Factor $2$ out of $2 (3) + 2 (i \sqrt{15})$ .

$\frac{2 (3 + i \sqrt{15})}{2}$

Step 2.4

Cancel the common factors.

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Step 2.4.1

Factor $2$ out of $2$ .

$\frac{2 (3 + i \sqrt{15})}{2 (1)}$

Step 2.4.2

Cancel the common factor.

$\frac{2 (3 + i \sqrt{15})}{2 \cdot 1}$

Step 2.4.3

Rewrite the expression.

$\frac{3 + i \sqrt{15}}{1}$

Step 2.4.4

Divide $3 + i \sqrt{15}$ by $1$ .

$3 + i \sqrt{15}$