Algebra Examples

$\frac{- 6 + - \sqrt{6^{2} - 4 \cdot 2 \cdot - 8}}{2 (2)}$

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 $1 \cdot - 1 = - 1$

$\frac{- 6 - \sqrt{6^{2} - 4 \cdot 2 \cdot - 8}}{2 (2)}$

Step 2

Simplify the numerator.

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Step 2.1

Raise $6$ to the power of $2$ .

$\frac{- 6 - \sqrt{36 - 4 \cdot 2 \cdot - 8}}{2 (2)}$

Step 2.2

Multiply $- 4 \cdot 2 \cdot - 8$ .

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Step 2.2.1

Multiply $- 4$ by $2$ .

$\frac{- 6 - \sqrt{36 - 8 \cdot - 8}}{2 (2)}$

Step 2.2.2

Multiply $- 8$ by $- 8$ .

$\frac{- 6 - \sqrt{36 + 64}}{2 (2)}$

Step 2.3

Add $36$ and $64$ .

$\frac{- 6 - \sqrt{100}}{2 (2)}$

Step 2.4

Rewrite $100$ as $10^{2}$ .

$\frac{- 6 - \sqrt{10^{2}}}{2 (2)}$

Step 2.5

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

$\frac{- 6 - 1 \cdot 10}{2 (2)}$

Step 2.6

Multiply $- 1$ by $10$ .

$\frac{- 6 - 10}{2 (2)}$

Step 2.7

Subtract $10$ from $- 6$ .

$\frac{- 16}{2 (2)}$

Step 3

Simplify the expression.

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Step 3.1

Multiply $2$ by $2$ .

$\frac{- 16}{4}$

Step 3.2

Divide $- 16$ by $4$ .

$- 4$