Evaluate (-3+- square root of (3)^2+4(10)(2))/(2(10))

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

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 $1 \cdot - 1 = - 1$

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

Step 2

Simplify the numerator.

Raise $3$ to the power of $2$ .

$\frac{- 3 - \sqrt{9 + 4 (10) \cdot 2}}{2 (10)}$

Multiply $4 (10) \cdot 2$ .

Multiply $4$ by $10$ .

$\frac{- 3 - \sqrt{9 + 40 \cdot 2}}{2 (10)}$

Multiply $40$ by $2$ .

$\frac{- 3 - \sqrt{9 + 80}}{2 (10)}$

Add $9$ and $80$ .

$\frac{- 3 - \sqrt{89}}{2 (10)}$

Step 3

Simplify with factoring out.

Multiply $2$ by $10$ .

$\frac{- 3 - \sqrt{89}}{20}$

Rewrite $- 3$ as $- 1 (3)$ .

$\frac{- 1 (3) - \sqrt{89}}{20}$

Factor $- 1$ out of $- \sqrt{89}$ .

$\frac{- 1 (3) - (\sqrt{89})}{20}$

Factor $- 1$ out of $- 1 (3) - (\sqrt{89})$ .

$\frac{- 1 (3 + \sqrt{89})}{20}$

Move the negative in front of the fraction.

$- \frac{3 + \sqrt{89}}{20}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{3 + \sqrt{89}}{20}$

Decimal Form:

$- 0.62169905 \dots$

Evaluate (-3+- square root of (3)^2+4(10)(2))/(2(10))

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