Evaluate (-20+ square root of -75)/40

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Algebra

$\frac{- 20 + \sqrt{- 75}}{40}$

Pull out imaginary unit $i$ .

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Rewrite $- 75$ as $- 1 (75)$ .

$\frac{- 20 + \sqrt{- 1 (75)}}{40}$

Rewrite $\sqrt{- 1 (75)}$ as $\sqrt{- 1} \cdot \sqrt{75}$ .

$\frac{- 20 + \sqrt{- 1} \cdot \sqrt{75}}{40}$

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

$\frac{- 20 + i \cdot \sqrt{75}}{40}$

Simplify the numerator.

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Rewrite $75$ as $5^{2} \cdot 3$ .

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Factor $25$ out of $75$ .

$\frac{- 20 + i \cdot \sqrt{25 (3)}}{40}$

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

$\frac{- 20 + i \cdot \sqrt{5^{2} \cdot 3}}{40}$

Pull terms out from under the radical.

$\frac{- 20 + i \cdot (5 \sqrt{3})}{40}$

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

$\frac{- 20 + 5 i \sqrt{3}}{40}$

Simplify terms.

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Cancel the common factor of $- 20 + 5 i \sqrt{3}$ and $40$ .

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Factor $5$ out of $- 20$ .

$\frac{5 \cdot - 4 + 5 i \sqrt{3}}{40}$

Factor $5$ out of $5 i \sqrt{3}$ .

$\frac{5 \cdot - 4 + 5 (i \sqrt{3})}{40}$

Factor $5$ out of $5 \cdot - 4 + 5 (i \sqrt{3})$ .

$\frac{5 \cdot (- 4 + i \sqrt{3})}{40}$

Cancel the common factors.

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Factor $5$ out of $40$ .

$\frac{5 \cdot (- 4 + i \sqrt{3})}{5 (8)}$

Cancel the common factor.

$\frac{5 \cdot (- 4 + i \sqrt{3})}{5 \cdot 8}$

Rewrite the expression.

$\frac{- 4 + i \sqrt{3}}{8}$

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

$\frac{- 1 (4) + i \sqrt{3}}{8}$

Factor $- 1$ out of $i \sqrt{3}$ .

$\frac{- 1 (4) - (- i \sqrt{3})}{8}$

Factor $- 1$ out of $- 1 (4) - (- i \sqrt{3})$ .

$\frac{- 1 (4 - i \sqrt{3})}{8}$

Move the negative in front of the fraction.

$- \frac{4 - i \sqrt{3}}{8}$

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Name

Name	five hundred seventy-seven million sixty-nine thousand eight hundred eighty-seven

Interesting facts

577069887 has 4 divisors, whose sum is 769426520
The reverse of 577069887 is 788960775
Previous prime number is 3

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 57
Digital Root 3

Name

Name	one billion four hundred ten million two hundred sixty-seven thousand two hundred ninety-seven

Interesting facts

1410267297 has 8 divisors, whose sum is 1880641600
The reverse of 1410267297 is 7927620141
Previous prime number is 7351

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 39
Digital Root 3

Name

Name	three hundred fifty-four million six hundred seventy-seven thousand nine hundred sixty-seven

Interesting facts

354677967 has 64 divisors, whose sum is 689452544
The reverse of 354677967 is 769776453
Previous prime number is 37

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 54
Digital Root 9

Solve Using the Quadratic Formula x^2-6x+5=0

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Multiply (7- square root of 2)(8+ square root of 2)

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Solve by Completing the Square x^2+22x=31