Algebra Examples

$\frac{- 6 + - \sqrt{36 - (4) \cdot 2 \cdot - 5}}{4}$

Step 1

Replace all occurrences of $+$ $-$ with a single $-$ . A plus sign followed by a minus sign has the same mathematical meaning as a single minus sign because $1 \cdot - 1 = - 1$

$\frac{- 6 - \sqrt{36 - 4 \cdot 2 \cdot - 5}}{4}$

Step 2

Simplify the numerator.

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Step 2.1

Multiply $- 4 \cdot 2 \cdot - 5$ .

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Step 2.1.1

Multiply $- 4$ by $2$ .

$\frac{- 6 - \sqrt{36 - 8 \cdot - 5}}{4}$

Step 2.1.2

Multiply $- 8$ by $- 5$ .

$\frac{- 6 - \sqrt{36 + 40}}{4}$

Step 2.2

Add $36$ and $40$ .

$\frac{- 6 - \sqrt{76}}{4}$

Step 2.3

Rewrite $76$ as $2^{2} \cdot 19$ .

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Step 2.3.1

Factor $4$ out of $76$ .

$\frac{- 6 - \sqrt{4 (19)}}{4}$

Step 2.3.2

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

$\frac{- 6 - \sqrt{2^{2} \cdot 19}}{4}$

Step 2.4

Pull terms out from under the radical.

$\frac{- 6 - (2 \sqrt{19})}{4}$

Step 2.5

Multiply $2$ by $- 1$ .

$\frac{- 6 - 2 \sqrt{19}}{4}$

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $- 6 - 2 \sqrt{19}$ and $4$ .

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Step 3.1.1

Factor $2$ out of $- 6$ .

$\frac{2 (- 3) - 2 \sqrt{19}}{4}$

Step 3.1.2

Factor $2$ out of $- 2 \sqrt{19}$ .

$\frac{2 (- 3) + 2 (- \sqrt{19})}{4}$

Step 3.1.3

Factor $2$ out of $2 (- 3) + 2 (- \sqrt{19})$ .

$\frac{2 (- 3 - \sqrt{19})}{4}$

Step 3.1.4

Cancel the common factors.

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Step 3.1.4.1

Factor $2$ out of $4$ .

$\frac{2 (- 3 - \sqrt{19})}{2 \cdot 2}$

Step 3.1.4.2

Cancel the common factor.

$\frac{2 (- 3 - \sqrt{19})}{2 \cdot 2}$

Step 3.1.4.3

Rewrite the expression.

$\frac{- 3 - \sqrt{19}}{2}$

Step 3.2

Rewrite $- 3$ as $- 1 (3)$ .

$\frac{- 1 (3) - \sqrt{19}}{2}$

Step 3.3

Factor $- 1$ out of $- \sqrt{19}$ .

$\frac{- 1 (3) - (\sqrt{19})}{2}$

Step 3.4

Factor $- 1$ out of $- 1 (3) - (\sqrt{19})$ .

$\frac{- 1 (3 + \sqrt{19})}{2}$

Step 3.5

Move the negative in front of the fraction.

$- \frac{3 + \sqrt{19}}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{3 + \sqrt{19}}{2}$

Decimal Form:

$- 3.67944947 \dots$