Algebra Examples

$\frac{2 + - \sqrt{4 - (4) \cdot 6 \cdot - 5}}{12}$

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 $1 \cdot - 1 = - 1$

$\frac{2 - \sqrt{4 - 4 \cdot 6 \cdot - 5}}{12}$

Step 2

Simplify the numerator.

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Step 2.1

Multiply $- 4 \cdot 6 \cdot - 5$ .

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Step 2.1.1

Multiply $- 4$ by $6$ .

$\frac{2 - \sqrt{4 - 24 \cdot - 5}}{12}$

Step 2.1.2

Multiply $- 24$ by $- 5$ .

$\frac{2 - \sqrt{4 + 120}}{12}$

Step 2.2

Add $4$ and $120$ .

$\frac{2 - \sqrt{124}}{12}$

Step 2.3

Rewrite $124$ as $2^{2} \cdot 31$ .

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Step 2.3.1

Factor $4$ out of $124$ .

$\frac{2 - \sqrt{4 (31)}}{12}$

Step 2.3.2

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

$\frac{2 - \sqrt{2^{2} \cdot 31}}{12}$

Step 2.4

Pull terms out from under the radical.

$\frac{2 - (2 \sqrt{31})}{12}$

Step 2.5

Multiply $2$ by $- 1$ .

$\frac{2 - 2 \sqrt{31}}{12}$

Step 3

Cancel the common factor of $2 - 2 \sqrt{31}$ and $12$ .

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Step 3.1

Factor $2$ out of $2$ .

$\frac{2 (1) - 2 \sqrt{31}}{12}$

Step 3.2

Factor $2$ out of $- 2 \sqrt{31}$ .

$\frac{2 (1) + 2 (- \sqrt{31})}{12}$

Step 3.3

Factor $2$ out of $2 (1) + 2 (- \sqrt{31})$ .

$\frac{2 (1 - \sqrt{31})}{12}$

Step 3.4

Cancel the common factors.

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Step 3.4.1

Factor $2$ out of $12$ .

$\frac{2 (1 - \sqrt{31})}{2 \cdot 6}$

Step 3.4.2

Cancel the common factor.

$\frac{2 (1 - \sqrt{31})}{2 \cdot 6}$

Step 3.4.3

Rewrite the expression.

$\frac{1 - \sqrt{31}}{6}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1 - \sqrt{31}}{6}$

Decimal Form:

$- 0.76129406 \dots$