4c^2+4c+1=15

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Solution for 4c^2+4c+1=15 equation: 


Simplifying
4c2 + 4c + 1 = 15

Reorder the terms:
1 + 4c + 4c2 = 15

Solving
1 + 4c + 4c2 = 15

Solving for variable 'c'.

Reorder the terms:
1 + -15 + 4c + 4c2 = 15 + -15

Combine like terms: 1 + -15 = -14
-14 + 4c + 4c2 = 15 + -15

Combine like terms: 15 + -15 = 0
-14 + 4c + 4c2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 2c + 2c2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + 2c + 2c2)' equal to zero and attempt to solve:

Simplifying
-7 + 2c + 2c2 = 0

Solving
-7 + 2c + 2c2 = 0

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

Divide each side by '2'.
-3.5 + c + c2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + c + 3.5 + c2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + c + c2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + c + c2 = 0 + 3.5
c + c2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
c + c2 = 3.5

The c term is c.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + c2 = 3.5 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + c2 = 3.5 + 0.25

Combine like terms: 3.5 + 0.25 = 3.75
1.25 + c2 = 3.75

Factor a perfect square on the left side:
(c + 0.5)(c + 0.5) = 3.75

Calculate the square root of the right side: 1.936491673

Break this problem into two subproblems by setting 
(c + 0.5) equal to 1.936491673 and -1.936491673.


Subproblem 1
c + 0.5 = 1.936491673

Simplifying
c + 0.5 = 1.936491673

Reorder the terms:
0.5 + c = 1.936491673

Solving
0.5 + c = 1.936491673

Solving for variable 'c'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + c = 1.936491673 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + c = 1.936491673 + -0.5
c = 1.936491673 + -0.5

Combine like terms: 1.936491673 + -0.5 = 1.436491673
c = 1.436491673

Simplifying
c = 1.436491673


Subproblem 2
c + 0.5 = -1.936491673

Simplifying
c + 0.5 = -1.936491673

Reorder the terms:
0.5 + c = -1.936491673

Solving
0.5 + c = -1.936491673

Solving for variable 'c'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + c = -1.936491673 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + c = -1.936491673 + -0.5
c = -1.936491673 + -0.5

Combine like terms: -1.936491673 + -0.5 = -2.436491673
c = -2.436491673

Simplifying
c = -2.436491673


Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {1.436491673, -2.436491673}
Solution
c = {1.436491673, -2.436491673}

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