Evaluate (-6+- square root of 6^2-42-8)/(2(2))

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

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.

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

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

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

Multiply $- 4$ by $2$ .

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

Multiply $- 8$ by $- 8$ .

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

Add $36$ and $64$ .

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

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

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

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

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

Multiply $- 1$ by $10$ .

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

Subtract $10$ from $- 6$ .

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

Step 3

Simplify the expression.

Multiply $2$ by $2$ .

$\frac{- 16}{4}$

Divide $- 16$ by $4$ .

$- 4$

Evaluate (-6+- square root of 6^2-4*2*-8)/(2(2))

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Evaluate (-6+- square root of 6^2-42-8)/(2(2))