Finite Math Examples

$\frac{\sqrt{50^{2} - 4 \cdot 1 \cdot 3825}}{2}$

Step 1

Simplify the numerator.

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Step 1.1

Raise $50$ to the power of $2$ .

$\frac{\sqrt{2500 - 4 \cdot 1 \cdot 3825}}{2}$

Step 1.2

Multiply $- 4 \cdot 1 \cdot 3825$ .

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Step 1.2.1

Multiply $- 4$ by $1$ .

$\frac{\sqrt{2500 - 4 \cdot 3825}}{2}$

Step 1.2.2

Multiply $- 4$ by $3825$ .

$\frac{\sqrt{2500 - 15300}}{2}$

$\frac{\sqrt{2500 - 15300}}{2}$

Step 1.3

Subtract $15300$ from $2500$ .

$\frac{\sqrt{- 12800}}{2}$

Step 1.4

Rewrite $- 12800$ as $- 1 (12800)$ .

$\frac{\sqrt{- 1 (12800)}}{2}$

Step 1.5

Rewrite $\sqrt{- 1 (12800)}$ as $\sqrt{- 1} \cdot \sqrt{12800}$ .

$\frac{\sqrt{- 1} \cdot \sqrt{12800}}{2}$

Step 1.6

Rewrite $\sqrt{- 1}$ as $i$ .

$\frac{i \cdot \sqrt{12800}}{2}$

Step 1.7

Rewrite $12800$ as $80^{2} \cdot 2$ .

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Step 1.7.1

Factor $6400$ out of $12800$ .

$\frac{i \cdot \sqrt{6400 (2)}}{2}$

Step 1.7.2

Rewrite $6400$ as $80^{2}$ .

$\frac{i \cdot \sqrt{80^{2} \cdot 2}}{2}$

$\frac{i \cdot \sqrt{80^{2} \cdot 2}}{2}$

Step 1.8

Pull terms out from under the radical.

$\frac{i \cdot (80 \sqrt{2})}{2}$

Step 1.9

Move $80$ to the left of $i$ .

$\frac{80 i \sqrt{2}}{2}$

$\frac{80 i \sqrt{2}}{2}$

Step 2

Cancel the common factor of $80$ and $2$ .

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Step 2.1

Factor $2$ out of $80 i \sqrt{2}$ .

$\frac{2 (40 i \sqrt{2})}{2}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $2$ out of $2$ .

$\frac{2 (40 i \sqrt{2})}{2 (1)}$

Step 2.2.2

Cancel the common factor.

$\frac{2 (40 i \sqrt{2})}{2 \cdot 1}$

Step 2.2.3

Rewrite the expression.

$\frac{40 i \sqrt{2}}{1}$

Step 2.2.4

Divide $40 i \sqrt{2}$ by $1$ .

$40 i \sqrt{2}$

$40 i \sqrt{2}$

$40 i \sqrt{2}$

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