4c^2-126c+900=0

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Solution for 4c^2-126c+900=0 equation: 


Simplifying
4c2 + -126c + 900 = 0

Reorder the terms:
900 + -126c + 4c2 = 0

Solving
900 + -126c + 4c2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '2'.
2(450 + -63c + 2c2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(450 + -63c + 2c2)' equal to zero and attempt to solve:

Simplifying
450 + -63c + 2c2 = 0

Solving
450 + -63c + 2c2 = 0

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

Divide each side by '2'.
225 + -31.5c + c2 = 0

Move the constant term to the right:

Add '-225' to each side of the equation.
225 + -31.5c + -225 + c2 = 0 + -225

Reorder the terms:
225 + -225 + -31.5c + c2 = 0 + -225

Combine like terms: 225 + -225 = 0
0 + -31.5c + c2 = 0 + -225
-31.5c + c2 = 0 + -225

Combine like terms: 0 + -225 = -225
-31.5c + c2 = -225

The c term is -31.5c.  Take half its coefficient (-15.75).
Square it (248.0625) and add it to both sides.

Add '248.0625' to each side of the equation.
-31.5c + 248.0625 + c2 = -225 + 248.0625

Reorder the terms:
248.0625 + -31.5c + c2 = -225 + 248.0625

Combine like terms: -225 + 248.0625 = 23.0625
248.0625 + -31.5c + c2 = 23.0625

Factor a perfect square on the left side:
(c + -15.75)(c + -15.75) = 23.0625

Calculate the square root of the right side: 4.802343178

Break this problem into two subproblems by setting 
(c + -15.75) equal to 4.802343178 and -4.802343178.


Subproblem 1
c + -15.75 = 4.802343178

Simplifying
c + -15.75 = 4.802343178

Reorder the terms:
-15.75 + c = 4.802343178

Solving
-15.75 + c = 4.802343178

Solving for variable 'c'.

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

Add '15.75' to each side of the equation.
-15.75 + 15.75 + c = 4.802343178 + 15.75

Combine like terms: -15.75 + 15.75 = 0.00
0.00 + c = 4.802343178 + 15.75
c = 4.802343178 + 15.75

Combine like terms: 4.802343178 + 15.75 = 20.552343178
c = 20.552343178

Simplifying
c = 20.552343178


Subproblem 2
c + -15.75 = -4.802343178

Simplifying
c + -15.75 = -4.802343178

Reorder the terms:
-15.75 + c = -4.802343178

Solving
-15.75 + c = -4.802343178

Solving for variable 'c'.

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

Add '15.75' to each side of the equation.
-15.75 + 15.75 + c = -4.802343178 + 15.75

Combine like terms: -15.75 + 15.75 = 0.00
0.00 + c = -4.802343178 + 15.75
c = -4.802343178 + 15.75

Combine like terms: -4.802343178 + 15.75 = 10.947656822
c = 10.947656822

Simplifying
c = 10.947656822


Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {20.552343178, 10.947656822}
Solution
c = {20.552343178, 10.947656822}

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