Algebra Examples

$\frac{- 5 + - \sqrt{25 - (4) \cdot 2 \cdot 6}}{- 10}$

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 $1 \cdot - 1 = - 1$

$\frac{- 5 - \sqrt{25 - 4 \cdot 2 \cdot 6}}{- 10}$

Step 2

Simplify the numerator.

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Step 2.1

Multiply $- 4 \cdot 2 \cdot 6$ .

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Step 2.1.1

Multiply $- 4$ by $2$ .

$\frac{- 5 - \sqrt{25 - 8 \cdot 6}}{- 10}$

Step 2.1.2

Multiply $- 8$ by $6$ .

$\frac{- 5 - \sqrt{25 - 48}}{- 10}$

Step 2.2

Subtract $48$ from $25$ .

$\frac{- 5 - \sqrt{- 23}}{- 10}$

Step 2.3

Rewrite $- 23$ as $- 1 (23)$ .

$\frac{- 5 - \sqrt{- 1 (23)}}{- 10}$

Step 2.4

Rewrite $\sqrt{- 1 (23)}$ as $\sqrt{- 1} \cdot \sqrt{23}$ .

$\frac{- 5 - (\sqrt{- 1} \cdot \sqrt{23})}{- 10}$

Step 2.5

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

$\frac{- 5 - i \sqrt{23}}{- 10}$

Step 3

Simplify with factoring out.

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Step 3.1

Move the negative in front of the fraction.

$- \frac{- 5 - i \sqrt{23}}{10}$

Step 3.2

Rewrite $- 5$ as $- 1 (5)$ .

$- \frac{- 1 (5) - i \sqrt{23}}{10}$

Step 3.3

Factor $- 1$ out of $- i \sqrt{23}$ .

$- \frac{- 1 (5) - (i \sqrt{23})}{10}$

Step 3.4

Factor $- 1$ out of $- 1 (5) - (i \sqrt{23})$ .

$- \frac{- 1 (5 + i \sqrt{23})}{10}$

Step 3.5

Simplify the expression.

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Step 3.5.1

Move the negative in front of the fraction.

$- - \frac{5 + i \sqrt{23}}{10}$

Step 3.5.2

Multiply $- 1$ by $- 1$ .

$1 \frac{5 + i \sqrt{23}}{10}$

Step 3.5.3

Multiply $\frac{5 + i \sqrt{23}}{10}$ by $1$ .

$\frac{5 + i \sqrt{23}}{10}$