Simplify (-(-10)+- square root of (-10)^2-43-1)/(2(3))

$\frac{- (- 10) + - \sqrt{{(- 10)}^{2} - 4 \cdot 3 \cdot - 1}}{2 (3)}$

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 $1 \cdot - 1 = - 1$

$\frac{- (- 10) - \sqrt{{(- 10)}^{2} - 4 \cdot 3 \cdot - 1}}{2 (3)}$

Simplify the numerator.

Multiply $- 1$ by $- 10$ .

$\frac{10 - \sqrt{{(- 10)}^{2} - 4 \cdot 3 \cdot - 1}}{2 (3)}$

Raise $- 10$ to the power of $2$ .

$\frac{10 - \sqrt{100 - 4 \cdot 3 \cdot - 1}}{2 (3)}$

Multiply $- 4$ by $3$ .

$\frac{10 - \sqrt{100 - 12 \cdot - 1}}{2 (3)}$

Multiply $- 12$ by $- 1$ .

$\frac{10 - \sqrt{100 + 12}}{2 (3)}$

Add $100$ and $12$ .

$\frac{10 - \sqrt{112}}{2 (3)}$

Rewrite $112$ as $4^{2} \cdot 7$ .

Factor $16$ out of $112$ .

$\frac{10 - \sqrt{16 (7)}}{2 (3)}$

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

$\frac{10 - \sqrt{4^{2} \cdot 7}}{2 (3)}$

Pull terms out from under the radical.

$\frac{10 - (4 \sqrt{7})}{2 (3)}$

Multiply $4$ by $- 1$ .

$\frac{10 - 4 \sqrt{7}}{2 (3)}$

Reduce the expression by cancelling the common factors.

Multiply $2$ by $3$ .

$\frac{10 - 4 \sqrt{7}}{6}$

Cancel the common factor of $10 - 4 \sqrt{7}$ and $6$ .

Factor $2$ out of $10$ .

$\frac{2 (5) - 4 \sqrt{7}}{6}$

Factor $2$ out of $- 4 \sqrt{7}$ .

$\frac{2 (5) + 2 (- 2 \sqrt{7})}{6}$

Factor $2$ out of $2 (5) + 2 (- 2 \sqrt{7})$ .

$\frac{2 (5 - 2 \sqrt{7})}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

$\frac{2 (5 - 2 \sqrt{7})}{2 \cdot 3}$

Cancel the common factor.

$\frac{2 (5 - 2 \sqrt{7})}{2 \cdot 3}$

Rewrite the expression.

$\frac{5 - 2 \sqrt{7}}{3}$

The result can be shown in multiple forms.

Exact Form:

$\frac{5 - 2 \sqrt{7}}{3}$

Decimal Form:

$- 0.09716754 \dots$

Simplify (-(-10)+- square root of (-10)^2-4*3*-1)/(2(3))

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Simplify (-(-10)+- square root of (-10)^2-43-1)/(2(3))