-200c^2+92000c-8400000=0

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Solution for -200c^2+92000c-8400000=0 equation: 


Simplifying
-200c2 + 92000c + -8400000 = 0

Reorder the terms:
-8400000 + 92000c + -200c2 = 0

Solving
-8400000 + 92000c + -200c2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '200'.
200(-42000 + 460c + -1c2) = 0

Ignore the factor 200.

Subproblem 1
Set the factor '(-42000 + 460c + -1c2)' equal to zero and attempt to solve:

Simplifying
-42000 + 460c + -1c2 = 0

Solving
-42000 + 460c + -1c2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
42000 + -460c + c2 = 0

Move the constant term to the right:

Add '-42000' to each side of the equation.
42000 + -460c + -42000 + c2 = 0 + -42000

Reorder the terms:
42000 + -42000 + -460c + c2 = 0 + -42000

Combine like terms: 42000 + -42000 = 0
0 + -460c + c2 = 0 + -42000
-460c + c2 = 0 + -42000

Combine like terms: 0 + -42000 = -42000
-460c + c2 = -42000

The c term is -460c.  Take half its coefficient (-230).
Square it (52900) and add it to both sides.

Add '52900' to each side of the equation.
-460c + 52900 + c2 = -42000 + 52900

Reorder the terms:
52900 + -460c + c2 = -42000 + 52900

Combine like terms: -42000 + 52900 = 10900
52900 + -460c + c2 = 10900

Factor a perfect square on the left side:
(c + -230)(c + -230) = 10900

Calculate the square root of the right side: 104.403065089

Break this problem into two subproblems by setting 
(c + -230) equal to 104.403065089 and -104.403065089.


Subproblem 1
c + -230 = 104.403065089

Simplifying
c + -230 = 104.403065089

Reorder the terms:
-230 + c = 104.403065089

Solving
-230 + c = 104.403065089

Solving for variable 'c'.

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

Add '230' to each side of the equation.
-230 + 230 + c = 104.403065089 + 230

Combine like terms: -230 + 230 = 0
0 + c = 104.403065089 + 230
c = 104.403065089 + 230

Combine like terms: 104.403065089 + 230 = 334.403065089
c = 334.403065089

Simplifying
c = 334.403065089


Subproblem 2
c + -230 = -104.403065089

Simplifying
c + -230 = -104.403065089

Reorder the terms:
-230 + c = -104.403065089

Solving
-230 + c = -104.403065089

Solving for variable 'c'.

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

Add '230' to each side of the equation.
-230 + 230 + c = -104.403065089 + 230

Combine like terms: -230 + 230 = 0
0 + c = -104.403065089 + 230
c = -104.403065089 + 230

Combine like terms: -104.403065089 + 230 = 125.596934911
c = 125.596934911

Simplifying
c = 125.596934911


Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {334.403065089, 125.596934911}
Solution
c = {334.403065089, 125.596934911}

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