Finite Math Examples

$x = \frac{- (- 8) - \sqrt{{(- 8)}^{2} - 4 \cdot 5 \cdot 3}}{2 (5)}$

Step 1

Simplify the numerator.

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Step 1.1

Multiply $- 1$ by $- 8$ .

$x = \frac{8 - \sqrt{{(- 8)}^{2} - 4 \cdot 5 \cdot 3}}{2 (5)}$

Step 1.2

Raise $- 8$ to the power of $2$ .

$x = \frac{8 - \sqrt{64 - 4 \cdot 5 \cdot 3}}{2 (5)}$

Step 1.3

Multiply $- 4 \cdot 5 \cdot 3$ .

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Step 1.3.1

Multiply $- 4$ by $5$ .

$x = \frac{8 - \sqrt{64 - 20 \cdot 3}}{2 (5)}$

Step 1.3.2

Multiply $- 20$ by $3$ .

$x = \frac{8 - \sqrt{64 - 60}}{2 (5)}$

Step 1.4

Subtract $60$ from $64$ .

$x = \frac{8 - \sqrt{4}}{2 (5)}$

Step 1.5

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

$x = \frac{8 - \sqrt{2^{2}}}{2 (5)}$

Step 1.6

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

$x = \frac{8 - 1 \cdot 2}{2 (5)}$

Step 1.7

Multiply $- 1$ by $2$ .

$x = \frac{8 - 2}{2 (5)}$

Step 1.8

Subtract $2$ from $8$ .

$x = \frac{6}{2 (5)}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Multiply $2$ by $5$ .

$x = \frac{6}{10}$

Step 2.2

Cancel the common factor of $6$ and $10$ .

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Step 2.2.1

Factor $2$ out of $6$ .

$x = \frac{2 (3)}{10}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $2$ out of $10$ .

$x = \frac{2 \cdot 3}{2 \cdot 5}$

Step 2.2.2.2

Cancel the common factor.

$x = \frac{2 \cdot 3}{2 \cdot 5}$

Step 2.2.2.3

Rewrite the expression.

$x = \frac{3}{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{5}$

Decimal Form:

$x = 0.6$