Finite Math Examples

$\frac{- 4 + \sqrt{16 - 4 \cdot 1 \cdot - 91}}{2}$

Step 1

Simplify the numerator.

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Step 1.1

Multiply $- 4 \cdot 1 \cdot - 91$ .

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Step 1.1.1

Multiply $- 4$ by $1$ .

$\frac{- 4 + \sqrt{16 - 4 \cdot - 91}}{2}$

Step 1.1.2

Multiply $- 4$ by $- 91$ .

$\frac{- 4 + \sqrt{16 + 364}}{2}$

$\frac{- 4 + \sqrt{16 + 364}}{2}$

Step 1.2

Add $16$ and $364$ .

$\frac{- 4 + \sqrt{380}}{2}$

Step 1.3

Rewrite $380$ as $2^{2} \cdot 95$ .

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Step 1.3.1

Factor $4$ out of $380$ .

$\frac{- 4 + \sqrt{4 (95)}}{2}$

Step 1.3.2

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

$\frac{- 4 + \sqrt{2^{2} \cdot 95}}{2}$

$\frac{- 4 + \sqrt{2^{2} \cdot 95}}{2}$

Step 1.4

Pull terms out from under the radical.

$\frac{- 4 + 2 \sqrt{95}}{2}$

$\frac{- 4 + 2 \sqrt{95}}{2}$

Step 2

Cancel the common factor of $- 4 + 2 \sqrt{95}$ and $2$ .

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Step 2.1

Factor $2$ out of $- 4$ .

$\frac{2 \cdot - 2 + 2 \sqrt{95}}{2}$

Step 2.2

Factor $2$ out of $2 \sqrt{95}$ .

$\frac{2 \cdot - 2 + 2 (\sqrt{95})}{2}$

Step 2.3

Factor $2$ out of $2 (- 2) + 2 (\sqrt{95})$ .

$\frac{2 (- 2 + \sqrt{95})}{2}$

Step 2.4

Cancel the common factors.

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Step 2.4.1

Factor $2$ out of $2$ .

$\frac{2 (- 2 + \sqrt{95})}{2 (1)}$

Step 2.4.2

Cancel the common factor.

$\frac{2 (- 2 + \sqrt{95})}{2 \cdot 1}$

Step 2.4.3

Rewrite the expression.

$\frac{- 2 + \sqrt{95}}{1}$

Step 2.4.4

Divide $- 2 + \sqrt{95}$ by $1$ .

$- 2 + \sqrt{95}$

$- 2 + \sqrt{95}$

$- 2 + \sqrt{95}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 2 + \sqrt{95}$

Decimal Form:

$7.74679434 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$