Finite Math Examples

$\frac{1280 - \sqrt{- 1280 - 4 \cdot 120 \cdot 1500}}{240}$

Step 1

Multiply $- 4 \cdot 120 \cdot 1500$ .

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Step 1.1

Multiply $- 4$ by $120$ .

$\frac{1280 - \sqrt{- 1280 - 480 \cdot 1500}}{240}$

Step 1.2

Multiply $- 480$ by $1500$ .

$\frac{1280 - \sqrt{- 1280 - 720000}}{240}$

Step 2

Subtract $720000$ from $- 1280$ .

$\frac{1280 - \sqrt{- 721280}}{240}$

Step 3

Rewrite $- 721280$ as $- 1 (721280)$ .

$\frac{1280 - \sqrt{- 1 (721280)}}{240}$

Step 4

Rewrite $\sqrt{- 1 (721280)}$ as $\sqrt{- 1} \cdot \sqrt{721280}$ .

$\frac{1280 - (\sqrt{- 1} \cdot \sqrt{721280})}{240}$

Step 5

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

$\frac{1280 - (i \cdot \sqrt{721280})}{240}$

Step 6

Rewrite $721280$ as $56^{2} \cdot 230$ .

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Step 6.1

Factor $3136$ out of $721280$ .

$\frac{1280 - (i \cdot \sqrt{3136 (230)})}{240}$

Step 6.2

Rewrite $3136$ as $56^{2}$ .

$\frac{1280 - (i \cdot \sqrt{56^{2} \cdot 230})}{240}$

Step 7

Pull terms out from under the radical.

$\frac{1280 - (i (56 \sqrt{230}))}{240}$

Step 8

Remove parentheses.

$\frac{1280 - (i \cdot 56 \sqrt{230})}{240}$

Step 9

Move $56$ to the left of $i$ .

$\frac{1280 - (56 i \sqrt{230})}{240}$

Step 10

Multiply $56$ by $- 1$ .

$\frac{1280 - 56 (i \sqrt{230})}{240}$

Step 11

Remove parentheses.

$\frac{1280 - 56 i \sqrt{230}}{240}$

Step 12

Reduce the expression $\frac{1280 - 56 i \sqrt{230}}{240}$ by cancelling the common factors.

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Step 12.1

Factor $8$ out of $1280$ .

$\frac{8 (160) - 56 i \sqrt{230}}{240}$

Step 12.2

Factor $8$ out of $- 56 i \sqrt{230}$ .

$\frac{8 (160) + 8 (- 7 i \sqrt{230})}{240}$

Step 12.3

Factor $8$ out of $8 (160) + 8 (- 7 i \sqrt{230})$ .

$\frac{8 (160 - 7 i \sqrt{230})}{240}$

Step 12.4

Factor $8$ out of $240$ .

$\frac{8 (160 - 7 i \sqrt{230})}{8 \cdot 30}$

Step 12.5

Cancel the common factor.

$\frac{8 (160 - 7 i \sqrt{230})}{8 \cdot 30}$

Step 12.6

Rewrite the expression.

$\frac{160 - 7 i \sqrt{230}}{30}$