Evaluate (-20+ square root of -50)/60

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$\frac{- 20 + \sqrt{- 50}}{60}$

Pull out imaginary unit $i$ .

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Rewrite $- 50$ as $- 1 (50)$ .

$\frac{- 20 + \sqrt{- 1 (50)}}{60}$

Rewrite $\sqrt{- 1 (50)}$ as $\sqrt{- 1} \cdot \sqrt{50}$ .

$\frac{- 20 + \sqrt{- 1} \cdot \sqrt{50}}{60}$

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

$\frac{- 20 + i \cdot \sqrt{50}}{60}$

Simplify the numerator.

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Rewrite $50$ as $5^{2} \cdot 2$ .

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Factor $25$ out of $50$ .

$\frac{- 20 + i \cdot \sqrt{25 (2)}}{60}$

Rewrite $25$ as $5^{2}$ .

$\frac{- 20 + i \cdot \sqrt{5^{2} \cdot 2}}{60}$

Pull terms out from under the radical.

$\frac{- 20 + i \cdot (5 \sqrt{2})}{60}$

Move $5$ to the left of $i$ .

$\frac{- 20 + 5 i \sqrt{2}}{60}$

Simplify terms.

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Cancel the common factor of $- 20 + 5 i \sqrt{2}$ and $60$ .

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Factor $5$ out of $- 20$ .

$\frac{5 \cdot - 4 + 5 i \sqrt{2}}{60}$

Factor $5$ out of $5 i \sqrt{2}$ .

$\frac{5 \cdot - 4 + 5 (i \sqrt{2})}{60}$

Factor $5$ out of $5 \cdot - 4 + 5 (i \sqrt{2})$ .

$\frac{5 \cdot (- 4 + i \sqrt{2})}{60}$

Cancel the common factors.

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Factor $5$ out of $60$ .

$\frac{5 \cdot (- 4 + i \sqrt{2})}{5 (12)}$

Cancel the common factor.

$\frac{5 \cdot (- 4 + i \sqrt{2})}{5 \cdot 12}$

Rewrite the expression.

$\frac{- 4 + i \sqrt{2}}{12}$

Rewrite $- 4$ as $- 1 (4)$ .

$\frac{- 1 (4) + i \sqrt{2}}{12}$

Factor $- 1$ out of $i \sqrt{2}$ .

$\frac{- 1 (4) - (- i \sqrt{2})}{12}$

Factor $- 1$ out of $- 1 (4) - (- i \sqrt{2})$ .

$\frac{- 1 (4 - i \sqrt{2})}{12}$

Move the negative in front of the fraction.

$- \frac{4 - i \sqrt{2}}{12}$

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Name

Name	one hundred thirty-eight million two hundred seventy-four thousand eight hundred eleven

Interesting facts

138274811 has 4 divisors, whose sum is 138322800
The reverse of 138274811 is 118472831
Previous prime number is 3079

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 35
Digital Root 8

Name

Name	one billion two hundred ninety-three million seventy thousand six hundred eight

Interesting facts

1293070608 has 512 divisors, whose sum is 9937572480
The reverse of 1293070608 is 8060703921
Previous prime number is 73

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 36
Digital Root 9

Name

Name	seven hundred seventy-six million twenty-two thousand three hundred forty-three

Interesting facts

776022343 has 4 divisors, whose sum is 790664328
The reverse of 776022343 is 343220677
Previous prime number is 53

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 34
Digital Root 7

Solve Using the Quadratic Formula 3x^2-2x-5=0

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