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:

$x = 0.6$