Finite Math Examples

$\frac{- 5 \sqrt{{(5)}^{2} - 4 \cdot 3 \cdot - 2}}{2 (3)}$

Step 1

Simplify the numerator.

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Step 1.1

Raise $5$ to the power of $2$ .

$\frac{- 5 \sqrt{25 - 4 \cdot 3 \cdot - 2}}{2 (3)}$

Step 1.2

Multiply $- 4 \cdot 3 \cdot - 2$ .

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Step 1.2.1

Multiply $- 4$ by $3$ .

$\frac{- 5 \sqrt{25 - 12 \cdot - 2}}{2 (3)}$

Step 1.2.2

Multiply $- 12$ by $- 2$ .

$\frac{- 5 \sqrt{25 + 24}}{2 (3)}$

Step 1.3

Add $25$ and $24$ .

$\frac{- 5 \sqrt{49}}{2 (3)}$

Step 1.4

Rewrite $49$ as $7^{2}$ .

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

Step 1.5

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

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

Step 2

Simplify the expression.

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Step 2.1

Multiply $2$ by $3$ .

$\frac{- 5 \cdot 7}{6}$

Step 2.2

Multiply $- 5$ by $7$ .

$\frac{- 35}{6}$

Step 2.3

Move the negative in front of the fraction.

$- \frac{35}{6}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- \frac{35}{6}$

Decimal Form:

$- 5.8\overline{3}$

Mixed Number Form:

$- 5 \frac{5}{6}$