Basic Math Examples

$- (\sqrt{3} (2 \sqrt{7} - \frac{1}{2} \cdot \sqrt{7})) - 2 \sqrt{49}$

Step 1

Simplify each term.

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Step 1.1

Combine $\sqrt{7}$ and $\frac{1}{2}$ .

$- (\sqrt{3} (2 \sqrt{7} - \frac{\sqrt{7}}{2})) - 2 \sqrt{49}$

Step 1.2

To write $2 \sqrt{7}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- (\sqrt{3} (2 \sqrt{7} \cdot \frac{2}{2} - \frac{\sqrt{7}}{2})) - 2 \sqrt{49}$

Step 1.3

Combine $2 \sqrt{7}$ and $\frac{2}{2}$ .

$- (\sqrt{3} (\frac{2 \sqrt{7} \cdot 2}{2} - \frac{\sqrt{7}}{2})) - 2 \sqrt{49}$

Step 1.4

Combine the numerators over the common denominator.

$- (\sqrt{3} \frac{2 \sqrt{7} \cdot 2 - \sqrt{7}}{2}) - 2 \sqrt{49}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $2$ by $2$ .

$- (\sqrt{3} \frac{4 \sqrt{7} - \sqrt{7}}{2}) - 2 \sqrt{49}$

Step 1.5.2

Subtract $\sqrt{7}$ from $4 \sqrt{7}$ .

$- (\sqrt{3} \frac{3 \sqrt{7}}{2}) - 2 \sqrt{49}$

Step 1.6

Multiply $\sqrt{3} \frac{3 \sqrt{7}}{2}$ .

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Step 1.6.1

Combine $\sqrt{3}$ and $\frac{3 \sqrt{7}}{2}$ .

$- \frac{\sqrt{3} (3 \sqrt{7})}{2} - 2 \sqrt{49}$

Step 1.6.2

Combine using the product rule for radicals.

$- \frac{3 \sqrt{3 \cdot 7}}{2} - 2 \sqrt{49}$

Step 1.6.3

Multiply $3$ by $7$ .

$- \frac{3 \sqrt{21}}{2} - 2 \sqrt{49}$

Step 1.7

Rewrite $49$ as $7^{2}$ .

$- \frac{3 \sqrt{21}}{2} - 2 \sqrt{7^{2}}$

Step 1.8

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

$- \frac{3 \sqrt{21}}{2} - 2 \cdot 7$

Step 1.9

Multiply $- 2$ by $7$ .

$- \frac{3 \sqrt{21}}{2} - 14$

Step 2

To write $- 14$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{3 \sqrt{21}}{2} - 14 \cdot \frac{2}{2}$

Step 3

Combine $- 14$ and $\frac{2}{2}$ .

$- \frac{3 \sqrt{21}}{2} + \frac{- 14 \cdot 2}{2}$

Step 4

Simplify the expression.

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Step 4.1

Combine the numerators over the common denominator.

$\frac{- 3 \sqrt{21} - 14 \cdot 2}{2}$

Step 4.2

Multiply $- 14$ by $2$ .

$\frac{- 3 \sqrt{21} - 28}{2}$

Step 5

Factor $- 1$ out of $- 3 \sqrt{21}$ .

$\frac{- (3 \sqrt{21}) - 28}{2}$

Step 6

Rewrite $- 28$ as $- 1 (28)$ .

$\frac{- (3 \sqrt{21}) - 1 (28)}{2}$

Step 7

Factor $- 1$ out of $- (3 \sqrt{21}) - 1 (28)$ .

$\frac{- (3 \sqrt{21} + 28)}{2}$

Step 8

Simplify the expression.

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Step 8.1

Rewrite $- (3 \sqrt{21} + 28)$ as $- 1 (3 \sqrt{21} + 28)$ .

$\frac{- 1 (3 \sqrt{21} + 28)}{2}$

Step 8.2

Move the negative in front of the fraction.

$- \frac{3 \sqrt{21} + 28}{2}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$- \frac{3 \sqrt{21} + 28}{2}$

Decimal Form:

$- 20.87386354 \dots$