8c(2c-1)=56

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Solution for 8c(2c-1)=56 equation: 


Simplifying
8c(2c + -1) = 56

Reorder the terms:
8c(-1 + 2c) = 56
(-1 * 8c + 2c * 8c) = 56
(-8c + 16c2) = 56

Solving
-8c + 16c2 = 56

Solving for variable 'c'.

Reorder the terms:
-56 + -8c + 16c2 = 56 + -56

Combine like terms: 56 + -56 = 0
-56 + -8c + 16c2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-7 + -1c + 2c2) = 0

Ignore the factor 8.

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

Simplifying
-7 + -1c + 2c2 = 0

Solving
-7 + -1c + 2c2 = 0

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

Divide each side by '2'.
-3.5 + -0.5c + c2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + -0.5c + 3.5 + c2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + -0.5c + c2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + -0.5c + c2 = 0 + 3.5
-0.5c + c2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
-0.5c + c2 = 3.5

The c term is -0.5c.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5c + 0.0625 + c2 = 3.5 + 0.0625

Reorder the terms:
0.0625 + -0.5c + c2 = 3.5 + 0.0625

Combine like terms: 3.5 + 0.0625 = 3.5625
0.0625 + -0.5c + c2 = 3.5625

Factor a perfect square on the left side:
(c + -0.25)(c + -0.25) = 3.5625

Calculate the square root of the right side: 1.887458609

Break this problem into two subproblems by setting 
(c + -0.25) equal to 1.887458609 and -1.887458609.


Subproblem 1
c + -0.25 = 1.887458609

Simplifying
c + -0.25 = 1.887458609

Reorder the terms:
-0.25 + c = 1.887458609

Solving
-0.25 + c = 1.887458609

Solving for variable 'c'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + c = 1.887458609 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + c = 1.887458609 + 0.25
c = 1.887458609 + 0.25

Combine like terms: 1.887458609 + 0.25 = 2.137458609
c = 2.137458609

Simplifying
c = 2.137458609


Subproblem 2
c + -0.25 = -1.887458609

Simplifying
c + -0.25 = -1.887458609

Reorder the terms:
-0.25 + c = -1.887458609

Solving
-0.25 + c = -1.887458609

Solving for variable 'c'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + c = -1.887458609 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + c = -1.887458609 + 0.25
c = -1.887458609 + 0.25

Combine like terms: -1.887458609 + 0.25 = -1.637458609
c = -1.637458609

Simplifying
c = -1.637458609


Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {2.137458609, -1.637458609}
Solution
c = {2.137458609, -1.637458609}

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