(20+20i)x^2+(-3.82+21.66i)x+(12.5-21.65i)=0

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Solution for (20+20i)x^2+(-3.82+21.66i)x+(12.5-21.65i)=0 equation: 


Simplifying
(20 + 20i) * x2 + (-3.82 + 21.66i) * x + (12.5 + -21.65i) = 0

Reorder the terms for easier multiplication:
x2(20 + 20i) + (-3.82 + 21.66i) * x + (12.5 + -21.65i) = 0
(20 * x2 + 20i * x2) + (-3.82 + 21.66i) * x + (12.5 + -21.65i) = 0

Reorder the terms:
(20ix2 + 20x2) + (-3.82 + 21.66i) * x + (12.5 + -21.65i) = 0
(20ix2 + 20x2) + (-3.82 + 21.66i) * x + (12.5 + -21.65i) = 0

Reorder the terms for easier multiplication:
20ix2 + 20x2 + x(-3.82 + 21.66i) + (12.5 + -21.65i) = 0
20ix2 + 20x2 + (-3.82 * x + 21.66i * x) + (12.5 + -21.65i) = 0

Reorder the terms:
20ix2 + 20x2 + (21.66ix + -3.82x) + (12.5 + -21.65i) = 0
20ix2 + 20x2 + (21.66ix + -3.82x) + (12.5 + -21.65i) = 0

Remove parenthesis around (12.5 + -21.65i)
20ix2 + 20x2 + 21.66ix + -3.82x + 12.5 + -21.65i = 0

Reorder the terms:
12.5 + -21.65i + 21.66ix + 20ix2 + -3.82x + 20x2 = 0

Solving
12.5 + -21.65i + 21.66ix + 20ix2 + -3.82x + 20x2 = 0

Solving for variable 'i'.

Move all terms containing i to the left, all other terms to the right.

Add '-12.5' to each side of the equation.
12.5 + -21.65i + 21.66ix + 20ix2 + -3.82x + -12.5 + 20x2 = 0 + -12.5

Reorder the terms:
12.5 + -12.5 + -21.65i + 21.66ix + 20ix2 + -3.82x + 20x2 = 0 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + -21.65i + 21.66ix + 20ix2 + -3.82x + 20x2 = 0 + -12.5
-21.65i + 21.66ix + 20ix2 + -3.82x + 20x2 = 0 + -12.5

Combine like terms: 0 + -12.5 = -12.5
-21.65i + 21.66ix + 20ix2 + -3.82x + 20x2 = -12.5

Add '3.82x' to each side of the equation.
-21.65i + 21.66ix + 20ix2 + -3.82x + 3.82x + 20x2 = -12.5 + 3.82x

Combine like terms: -3.82x + 3.82x = 0.00
-21.65i + 21.66ix + 20ix2 + 0.00 + 20x2 = -12.5 + 3.82x
-21.65i + 21.66ix + 20ix2 + 20x2 = -12.5 + 3.82x

Add '-20x2' to each side of the equation.
-21.65i + 21.66ix + 20ix2 + 20x2 + -20x2 = -12.5 + 3.82x + -20x2

Combine like terms: 20x2 + -20x2 = 0
-21.65i + 21.66ix + 20ix2 + 0 = -12.5 + 3.82x + -20x2
-21.65i + 21.66ix + 20ix2 = -12.5 + 3.82x + -20x2

Reorder the terms:
12.5 + -21.65i + 21.66ix + 20ix2 + -3.82x + 20x2 = -12.5 + 3.82x + -20x2 + 12.5 + -3.82x + 20x2

Reorder the terms:
12.5 + -21.65i + 21.66ix + 20ix2 + -3.82x + 20x2 = -12.5 + 12.5 + 3.82x + -3.82x + -20x2 + 20x2

Combine like terms: -12.5 + 12.5 = 0.0
12.5 + -21.65i + 21.66ix + 20ix2 + -3.82x + 20x2 = 0.0 + 3.82x + -3.82x + -20x2 + 20x2
12.5 + -21.65i + 21.66ix + 20ix2 + -3.82x + 20x2 = 3.82x + -3.82x + -20x2 + 20x2

Combine like terms: 3.82x + -3.82x = 0.00
12.5 + -21.65i + 21.66ix + 20ix2 + -3.82x + 20x2 = 0.00 + -20x2 + 20x2
12.5 + -21.65i + 21.66ix + 20ix2 + -3.82x + 20x2 = -20x2 + 20x2

Combine like terms: -20x2 + 20x2 = 0
12.5 + -21.65i + 21.66ix + 20ix2 + -3.82x + 20x2 = 0

The solution to this equation could not be determined.

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