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

Subtract $40$ from $36$ .

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

Step 2.3

Rewrite $- 4$ as $- 1 (4)$ .

$\frac{6 - \sqrt{- 1 (4)}}{4}$

Step 2.4

Rewrite $\sqrt{- 1 (4)}$ as $\sqrt{- 1} \cdot \sqrt{4}$ .

$\frac{6 - (\sqrt{- 1} \cdot \sqrt{4})}{4}$

Step 2.5

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

$\frac{6 - (i \cdot \sqrt{4})}{4}$

Step 2.6

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

$\frac{6 - (i \cdot \sqrt{2^{2}})}{4}$

Step 2.7

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

$\frac{6 - (i \cdot 2)}{4}$

Step 2.8

Move $2$ to the left of $i$ .

$\frac{6 - (2 \cdot i)}{4}$

Step 2.9

Multiply $2$ by $- 1$ .

$\frac{6 - 2 i}{4}$

Step 3

Cancel the common factor of $6 - 2 i$ and $4$ .

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Step 3.1

Factor $2$ out of $6$ .

$\frac{2 (3) - 2 i}{4}$

Step 3.2

Factor $2$ out of $- 2 i$ .

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

Step 3.3

Factor $2$ out of $2 (3) + 2 (- i)$ .

$\frac{2 (3 - i)}{4}$

Step 3.4

Cancel the common factors.

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Step 3.4.1

Factor $2$ out of $4$ .

$\frac{2 (3 - i)}{2 \cdot 2}$

Step 3.4.2

Cancel the common factor.

$\frac{2 (3 - i)}{2 \cdot 2}$

Step 3.4.3

Rewrite the expression.

$\frac{3 - i}{2}$