Finite Math Examples

$x = \frac{- 16 + \sqrt{{(16)}^{2} - 4 \cdot - 12 \cdot 16}}{2 (- 12)}$

Step 1

Remove parentheses.

$x = \frac{- 16 + \sqrt{16^{2} - 4 \cdot - 12 \cdot 16}}{2 (- 12)}$

Step 2

Simplify $\frac{- 16 + \sqrt{16^{2} - 4 \cdot - 12 \cdot 16}}{2 (- 12)}$ .

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Step 2.1

Simplify the numerator.

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Step 2.1.1

Raise $16$ to the power of $2$ .

$x = \frac{- 16 + \sqrt{256 - 4 \cdot - 12 \cdot 16}}{2 (- 12)}$

Step 2.1.2

Multiply $- 4 \cdot - 12 \cdot 16$ .

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Step 2.1.2.1

Multiply $- 4$ by $- 12$ .

$x = \frac{- 16 + \sqrt{256 + 48 \cdot 16}}{2 (- 12)}$

Step 2.1.2.2

Multiply $48$ by $16$ .

$x = \frac{- 16 + \sqrt{256 + 768}}{2 (- 12)}$

Step 2.1.3

Add $256$ and $768$ .

$x = \frac{- 16 + \sqrt{1024}}{2 (- 12)}$

Step 2.1.4

Rewrite $1024$ as $32^{2}$ .

$x = \frac{- 16 + \sqrt{32^{2}}}{2 (- 12)}$

Step 2.1.5

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

$x = \frac{- 16 + 32}{2 (- 12)}$

Step 2.1.6

Add $- 16$ and $32$ .

$x = \frac{16}{2 (- 12)}$

Step 2.2

Reduce the expression by cancelling the common factors.

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Step 2.2.1

Multiply $2$ by $- 12$ .

$x = \frac{16}{- 24}$

Step 2.2.2

Cancel the common factor of $16$ and $- 24$ .

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Step 2.2.2.1

Factor $8$ out of $16$ .

$x = \frac{8 (2)}{- 24}$

Step 2.2.2.2

Cancel the common factors.

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Step 2.2.2.2.1

Factor $8$ out of $- 24$ .

$x = \frac{8 \cdot 2}{8 \cdot - 3}$

Step 2.2.2.2.2

Cancel the common factor.

$x = \frac{8 \cdot 2}{8 \cdot - 3}$

Step 2.2.2.2.3

Rewrite the expression.

$x = \frac{2}{- 3}$

Step 2.2.3

Move the negative in front of the fraction.

$x = - \frac{2}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{2}{3}$

Decimal Form:

$x = - 0.\overline{6}$