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

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Algebra

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

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	seven hundred nine million five hundred twenty-three thousand five hundred sixty-two

Interesting facts

709523562 has 32 divisors, whose sum is 1580995584
The reverse of 709523562 is 265325907
Previous prime number is 47

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 39
Digital Root 3

Name

Name	forty-two million one hundred forty-four thousand nine hundred forty-six

Interesting facts

42144946 has 16 divisors, whose sum is 66018240
The reverse of 42144946 is 64944124
Previous prime number is 107

Basic properties

Is Prime? no
Number parity even
Number length 8
Sum of Digits 34
Digital Root 7

Name

Name	one billion seven hundred fifty-nine million five hundred eighty-four thousand eight hundred ninety-five

Interesting facts

1759584895 has 8 divisors, whose sum is 2151341856
The reverse of 1759584895 is 5984859571
Previous prime number is 53

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 61
Digital Root 7

Evaluate log base 9 of 27

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

Solve Using the Quadratic Formula 2x^2-3x=7

Find Where Undefined/Discontinuous y=(x-3)/(x^2-12x+27)

Find the Vertex f(x)=1/2|x|-4/5