Simplify (-4+ square root of 32)/(-2(5))

$\frac{- 4 + \sqrt{32}}{- 2 (5)}$

Simplify the numerator.

Rewrite $32$ as $4^{2} \cdot 2$ .

Factor $16$ out of $32$ .

$\frac{- 4 + \sqrt{16 (2)}}{- 2 \cdot 5}$

Rewrite $16$ as $4^{2}$ .

$\frac{- 4 + \sqrt{4^{2} \cdot 2}}{- 2 \cdot 5}$

$\frac{- 4 + \sqrt{4^{2} \cdot 2}}{- 2 \cdot 5}$

Pull terms out from under the radical.

$\frac{- 4 + 4 \sqrt{2}}{- 2 \cdot 5}$

$\frac{- 4 + 4 \sqrt{2}}{- 2 \cdot 5}$

Simplify terms.

Multiply $- 2$ by $5$ .

$\frac{- 4 + 4 \sqrt{2}}{- 10}$

Cancel the common factor of $- 4 + 4 \sqrt{2}$ and $- 10$ .

Factor $2$ out of $- 4$ .

$\frac{2 (- 2) + 4 \sqrt{2}}{- 10}$

Factor $2$ out of $4 \sqrt{2}$ .

$\frac{2 (- 2) + 2 (2 \sqrt{2})}{- 10}$

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

$\frac{2 (- 2 + 2 \sqrt{2})}{- 10}$

Cancel the common factors.

Factor $2$ out of $- 10$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{- 2 + 2 \sqrt{2}}{- 5}$

$\frac{- 2 + 2 \sqrt{2}}{- 5}$

$\frac{- 2 + 2 \sqrt{2}}{- 5}$

Move the negative in front of the fraction.

$- \frac{- 2 + 2 \sqrt{2}}{5}$

Rewrite $- 2$ as $- 1 (2)$ .

$- \frac{- 1 (2) + 2 \sqrt{2}}{5}$

Factor $- 1$ out of $2 \sqrt{2}$ .

$- \frac{- 1 (2) - (- 2 \sqrt{2})}{5}$

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

$- \frac{- 1 (2 - 2 \sqrt{2})}{5}$

Simplify the expression.

Move the negative in front of the fraction.

$- - \frac{2 - 2 \sqrt{2}}{5}$

Multiply $- 1$ by $- 1$ .

$1 \frac{2 - 2 \sqrt{2}}{5}$

Multiply $\frac{2 - 2 \sqrt{2}}{5}$ by $1$ .

$\frac{2 - 2 \sqrt{2}}{5}$

$\frac{2 - 2 \sqrt{2}}{5}$

$\frac{2 - 2 \sqrt{2}}{5}$

The result can be shown in multiple forms.

Exact Form:

$\frac{2 - 2 \sqrt{2}}{5}$

Decimal Form:

$- 0.16568542 \dots$

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