Basic Math Examples

$\frac{- 50 + \sqrt{5692}}{4}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $5692$ as $2^{2} \cdot 1423$ .

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Step 1.1.1

Factor $4$ out of $5692$ .

$\frac{- 50 + \sqrt{4 (1423)}}{4}$

Step 1.1.2

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

$\frac{- 50 + \sqrt{2^{2} \cdot 1423}}{4}$

Step 1.2

Pull terms out from under the radical.

$\frac{- 50 + 2 \sqrt{1423}}{4}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $- 50 + 2 \sqrt{1423}$ and $4$ .

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Step 2.1.1

Factor $2$ out of $- 50$ .

$\frac{2 \cdot - 25 + 2 \sqrt{1423}}{4}$

Step 2.1.2

Factor $2$ out of $2 \sqrt{1423}$ .

$\frac{2 \cdot - 25 + 2 (\sqrt{1423})}{4}$

Step 2.1.3

Factor $2$ out of $2 \cdot - 25 + 2 (\sqrt{1423})$ .

$\frac{2 \cdot (- 25 + \sqrt{1423})}{4}$

Step 2.1.4

Cancel the common factors.

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Step 2.1.4.1

Factor $2$ out of $4$ .

$\frac{2 \cdot (- 25 + \sqrt{1423})}{2 (2)}$

Step 2.1.4.2

Cancel the common factor.

$\frac{2 \cdot (- 25 + \sqrt{1423})}{2 \cdot 2}$

Step 2.1.4.3

Rewrite the expression.

$\frac{- 25 + \sqrt{1423}}{2}$

Step 2.2

Rewrite $- 25$ as $- 1 (25)$ .

$\frac{- 1 (25) + \sqrt{1423}}{2}$

Step 2.3

Factor $- 1$ out of $\sqrt{1423}$ .

$\frac{- 1 (25) - 1 (- \sqrt{1423})}{2}$

Step 2.4

Factor $- 1$ out of $- 1 (25) - 1 (- \sqrt{1423})$ .

$\frac{- 1 (25 - \sqrt{1423})}{2}$

Step 2.5

Move the negative in front of the fraction.

$- \frac{25 - \sqrt{1423}}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- \frac{25 - \sqrt{1423}}{2}$

Decimal Form:

$6.36133611 \dots$