Algebra Examples

$\frac{30 - \sqrt{{(- 30)}^{2} - 4 \cdot - 16 \cdot 190}}{- 60}$

Step 1

Simplify the numerator.

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Step 1.1

Raise $- 30$ to the power of $2$ .

$\frac{30 - \sqrt{900 - 4 \cdot - 16 \cdot 190}}{- 60}$

Step 1.2

Multiply $- 4 \cdot - 16 \cdot 190$ .

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Step 1.2.1

Multiply $- 4$ by $- 16$ .

$\frac{30 - \sqrt{900 + 64 \cdot 190}}{- 60}$

Step 1.2.2

Multiply $64$ by $190$ .

$\frac{30 - \sqrt{900 + 12160}}{- 60}$

Step 1.3

Add $900$ and $12160$ .

$\frac{30 - \sqrt{13060}}{- 60}$

Step 1.4

Rewrite $13060$ as $2^{2} \cdot 3265$ .

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Step 1.4.1

Factor $4$ out of $13060$ .

$\frac{30 - \sqrt{4 (3265)}}{- 60}$

Step 1.4.2

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

$\frac{30 - \sqrt{2^{2} \cdot 3265}}{- 60}$

Step 1.5

Pull terms out from under the radical.

$\frac{30 - (2 \sqrt{3265})}{- 60}$

Step 1.6

Multiply $2$ by $- 1$ .

$\frac{30 - 2 \sqrt{3265}}{- 60}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $30 - 2 \sqrt{3265}$ and $- 60$ .

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Step 2.1.1

Factor $2$ out of $30$ .

$\frac{2 (15) - 2 \sqrt{3265}}{- 60}$

Step 2.1.2

Factor $2$ out of $- 2 \sqrt{3265}$ .

$\frac{2 (15) + 2 (- \sqrt{3265})}{- 60}$

Step 2.1.3

Factor $2$ out of $2 (15) + 2 (- \sqrt{3265})$ .

$\frac{2 (15 - \sqrt{3265})}{- 60}$

Step 2.1.4

Cancel the common factors.

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Step 2.1.4.1

Factor $2$ out of $- 60$ .

$\frac{2 (15 - \sqrt{3265})}{2 \cdot - 30}$

Step 2.1.4.2

Cancel the common factor.

$\frac{2 (15 - \sqrt{3265})}{2 \cdot - 30}$

Step 2.1.4.3

Rewrite the expression.

$\frac{15 - \sqrt{3265}}{- 30}$

Step 2.2

Move the negative in front of the fraction.

$- \frac{15 - \sqrt{3265}}{30}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- \frac{15 - \sqrt{3265}}{30}$

Decimal Form:

$1.40467261 \dots$