1180n^2-543980n+54070=0

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Solution for 1180n^2-543980n+54070=0 equation: 


Simplifying
1180n2 + -543980n + 54070 = 0

Reorder the terms:
54070 + -543980n + 1180n2 = 0

Solving
54070 + -543980n + 1180n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '10'.
10(5407 + -54398n + 118n2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(5407 + -54398n + 118n2)' equal to zero and attempt to solve:

Simplifying
5407 + -54398n + 118n2 = 0

Solving
5407 + -54398n + 118n2 = 0

Begin completing the square.  Divide all terms by
118 the coefficient of the squared term: 

Divide each side by '118'.
45.8220339 + -461n + n2 = 0

Move the constant term to the right:

Add '-45.8220339' to each side of the equation.
45.8220339 + -461n + -45.8220339 + n2 = 0 + -45.8220339

Reorder the terms:
45.8220339 + -45.8220339 + -461n + n2 = 0 + -45.8220339

Combine like terms: 45.8220339 + -45.8220339 = 0.0000000
0.0000000 + -461n + n2 = 0 + -45.8220339
-461n + n2 = 0 + -45.8220339

Combine like terms: 0 + -45.8220339 = -45.8220339
-461n + n2 = -45.8220339

The n term is -461n.  Take half its coefficient (-230.5).
Square it (53130.25) and add it to both sides.

Add '53130.25' to each side of the equation.
-461n + 53130.25 + n2 = -45.8220339 + 53130.25

Reorder the terms:
53130.25 + -461n + n2 = -45.8220339 + 53130.25

Combine like terms: -45.8220339 + 53130.25 = 53084.4279661
53130.25 + -461n + n2 = 53084.4279661

Factor a perfect square on the left side:
(n + -230.5)(n + -230.5) = 53084.4279661

Calculate the square root of the right side: 230.400581523

Break this problem into two subproblems by setting 
(n + -230.5) equal to 230.400581523 and -230.400581523.


Subproblem 1
n + -230.5 = 230.400581523

Simplifying
n + -230.5 = 230.400581523

Reorder the terms:
-230.5 + n = 230.400581523

Solving
-230.5 + n = 230.400581523

Solving for variable 'n'.

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

Add '230.5' to each side of the equation.
-230.5 + 230.5 + n = 230.400581523 + 230.5

Combine like terms: -230.5 + 230.5 = 0.0
0.0 + n = 230.400581523 + 230.5
n = 230.400581523 + 230.5

Combine like terms: 230.400581523 + 230.5 = 460.900581523
n = 460.900581523

Simplifying
n = 460.900581523


Subproblem 2
n + -230.5 = -230.400581523

Simplifying
n + -230.5 = -230.400581523

Reorder the terms:
-230.5 + n = -230.400581523

Solving
-230.5 + n = -230.400581523

Solving for variable 'n'.

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

Add '230.5' to each side of the equation.
-230.5 + 230.5 + n = -230.400581523 + 230.5

Combine like terms: -230.5 + 230.5 = 0.0
0.0 + n = -230.400581523 + 230.5
n = -230.400581523 + 230.5

Combine like terms: -230.400581523 + 230.5 = 0.099418477
n = 0.099418477

Simplifying
n = 0.099418477


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {460.900581523, 0.099418477}
Solution
n = {460.900581523, 0.099418477}

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