300i^2-2400i-3600=0

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Solution for 300i^2-2400i-3600=0 equation: 


Simplifying
300i2 + -2400i + -3600 = 0

Reorder the terms:
-3600 + -2400i + 300i2 = 0

Solving
-3600 + -2400i + 300i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '300'.
300(-12 + -8i + i2) = 0

Ignore the factor 300.

Subproblem 1
Set the factor '(-12 + -8i + i2)' equal to zero and attempt to solve:

Simplifying
-12 + -8i + i2 = 0

Solving
-12 + -8i + i2 = 0

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -8i + 12 + i2 = 0 + 12

Reorder the terms:
-12 + 12 + -8i + i2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -8i + i2 = 0 + 12
-8i + i2 = 0 + 12

Combine like terms: 0 + 12 = 12
-8i + i2 = 12

The i term is -8i.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8i + 16 + i2 = 12 + 16

Reorder the terms:
16 + -8i + i2 = 12 + 16

Combine like terms: 12 + 16 = 28
16 + -8i + i2 = 28

Factor a perfect square on the left side:
(i + -4)(i + -4) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(i + -4) equal to 5.291502622 and -5.291502622.


Subproblem 1
i + -4 = 5.291502622

Simplifying
i + -4 = 5.291502622

Reorder the terms:
-4 + i = 5.291502622

Solving
-4 + i = 5.291502622

Solving for variable 'i'.

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

Add '4' to each side of the equation.
-4 + 4 + i = 5.291502622 + 4

Combine like terms: -4 + 4 = 0
0 + i = 5.291502622 + 4
i = 5.291502622 + 4

Combine like terms: 5.291502622 + 4 = 9.291502622
i = 9.291502622

Simplifying
i = 9.291502622


Subproblem 2
i + -4 = -5.291502622

Simplifying
i + -4 = -5.291502622

Reorder the terms:
-4 + i = -5.291502622

Solving
-4 + i = -5.291502622

Solving for variable 'i'.

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

Add '4' to each side of the equation.
-4 + 4 + i = -5.291502622 + 4

Combine like terms: -4 + 4 = 0
0 + i = -5.291502622 + 4
i = -5.291502622 + 4

Combine like terms: -5.291502622 + 4 = -1.291502622
i = -1.291502622

Simplifying
i = -1.291502622


Solution
The solution to the problem is based on the solutions
from the subproblems.
i = {9.291502622, -1.291502622}
Solution
i = {9.291502622, -1.291502622}

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