Evaluate (-12+ square root of -45)/24

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$\frac{- 12 + \sqrt{- 45}}{24}$

Pull out imaginary unit $i$ .

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Rewrite $- 45$ as $- 1 (45)$ .

$\frac{- 12 + \sqrt{- 1 (45)}}{24}$

Rewrite $\sqrt{- 1 (45)}$ as $\sqrt{- 1} \cdot \sqrt{45}$ .

$\frac{- 12 + \sqrt{- 1} \cdot \sqrt{45}}{24}$

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

$\frac{- 12 + i \cdot \sqrt{45}}{24}$

Simplify the numerator.

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Rewrite $45$ as $3^{2} \cdot 5$ .

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Factor $9$ out of $45$ .

$\frac{- 12 + i \cdot \sqrt{9 (5)}}{24}$

Rewrite $9$ as $3^{2}$ .

$\frac{- 12 + i \cdot \sqrt{3^{2} \cdot 5}}{24}$

Pull terms out from under the radical.

$\frac{- 12 + i \cdot (3 \sqrt{5})}{24}$

Move $3$ to the left of $i$ .

$\frac{- 12 + 3 i \sqrt{5}}{24}$

Simplify terms.

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Cancel the common factor of $- 12 + 3 i \sqrt{5}$ and $24$ .

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Factor $3$ out of $- 12$ .

$\frac{3 \cdot - 4 + 3 i \sqrt{5}}{24}$

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

$\frac{3 \cdot - 4 + 3 (i \sqrt{5})}{24}$

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

$\frac{3 \cdot (- 4 + i \sqrt{5})}{24}$

Cancel the common factors.

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Factor $3$ out of $24$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{- 4 + i \sqrt{5}}{8}$

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

$\frac{- 1 (4) + i \sqrt{5}}{8}$

Factor $- 1$ out of $i \sqrt{5}$ .

$\frac{- 1 (4) - (- i \sqrt{5})}{8}$

Factor $- 1$ out of $- 1 (4) - (- i \sqrt{5})$ .

$\frac{- 1 (4 - i \sqrt{5})}{8}$

Move the negative in front of the fraction.

$- \frac{4 - i \sqrt{5}}{8}$

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Name

Name	one billion six hundred ninety-five million six hundred twenty-one thousand seven hundred ninety-three

Interesting facts

1695621793 has 8 divisors, whose sum is 1776297600
The reverse of 1695621793 is 3971265961
Previous prime number is 79

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 49
Digital Root 4

Name

Name	one billion nine million four hundred ninety-three thousand ninety-four

Interesting facts

1009493094 has 16 divisors, whose sum is 2024808768
The reverse of 1009493094 is 4903949001
Previous prime number is 347

Basic properties

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

Name

Name	one billion eight hundred eighty million five hundred eighty-six thousand one hundred fifty-three

Interesting facts

1880586153 has 16 divisors, whose sum is 3714738240
The reverse of 1880586153 is 3516850881
Previous prime number is 3

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 45
Digital Root 9

Factor x^2-5x+4

Evaluate 6/4

Solve by Factoring x^3+3x^2-4x-12=0

Find the X and Y Intercepts -x+4y=4

Solve Using the Quadratic Formula 4x^2-8=0