Basic Math Examples

$\frac{- (36) - \sqrt{{(36)}^{2} - 4 \cdot 1 \cdot 60}}{2}$

Step 1

Simplify the numerator.

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Step 1.1

Multiply $- 1$ by $36$ .

$\frac{- 36 - \sqrt{36^{2} - 4 \cdot 1 \cdot 60}}{2}$

Step 1.2

Raise $36$ to the power of $2$ .

$\frac{- 36 - \sqrt{1296 - 4 \cdot 1 \cdot 60}}{2}$

Step 1.3

Multiply $- 4 \cdot 1 \cdot 60$ .

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Step 1.3.1

Multiply $- 4$ by $1$ .

$\frac{- 36 - \sqrt{1296 - 4 \cdot 60}}{2}$

Step 1.3.2

Multiply $- 4$ by $60$ .

$\frac{- 36 - \sqrt{1296 - 240}}{2}$

Step 1.4

Subtract $240$ from $1296$ .

$\frac{- 36 - \sqrt{1056}}{2}$

Step 1.5

Rewrite $1056$ as $4^{2} \cdot 66$ .

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Step 1.5.1

Factor $16$ out of $1056$ .

$\frac{- 36 - \sqrt{16 (66)}}{2}$

Step 1.5.2

Rewrite $16$ as $4^{2}$ .

$\frac{- 36 - \sqrt{4^{2} \cdot 66}}{2}$

Step 1.6

Pull terms out from under the radical.

$\frac{- 36 - (4 \sqrt{66})}{2}$

Step 1.7

Multiply $4$ by $- 1$ .

$\frac{- 36 - 4 \sqrt{66}}{2}$

Step 2

Cancel the common factor of $- 36 - 4 \sqrt{66}$ and $2$ .

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Step 2.1

Factor $2$ out of $- 36$ .

$\frac{2 \cdot - 18 - 4 \sqrt{66}}{2}$

Step 2.2

Factor $2$ out of $- 4 \sqrt{66}$ .

$\frac{2 \cdot - 18 + 2 (- 2 \sqrt{66})}{2}$

Step 2.3

Factor $2$ out of $2 (- 18) + 2 (- 2 \sqrt{66})$ .

$\frac{2 (- 18 - 2 \sqrt{66})}{2}$

Step 2.4

Cancel the common factors.

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Step 2.4.1

Factor $2$ out of $2$ .

$\frac{2 (- 18 - 2 \sqrt{66})}{2 (1)}$

Step 2.4.2

Cancel the common factor.

$\frac{2 (- 18 - 2 \sqrt{66})}{2 \cdot 1}$

Step 2.4.3

Rewrite the expression.

$\frac{- 18 - 2 \sqrt{66}}{1}$

Step 2.4.4

Divide $- 18 - 2 \sqrt{66}$ by $1$ .

$- 18 - 2 \sqrt{66}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 18 - 2 \sqrt{66}$

Decimal Form:

$- 34.24807680 \dots$