6c^2-16c+2=0

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Solution for 6c^2-16c+2=0 equation:


Simplifying
6c2 + -16c + 2 = 0

Reorder the terms:
2 + -16c + 6c2 = 0

Solving
2 + -16c + 6c2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -8c + 3c2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + -8c + 3c2)' equal to zero and attempt to solve:

Simplifying
1 + -8c + 3c2 = 0

Solving
1 + -8c + 3c2 = 0

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

Divide each side by '3'.
0.3333333333 + -2.666666667c + c2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + -2.666666667c + -0.3333333333 + c2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + -2.666666667c + c2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + -2.666666667c + c2 = 0 + -0.3333333333
-2.666666667c + c2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
-2.666666667c + c2 = -0.3333333333

The c term is -2.666666667c.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667c + 1.777777780 + c2 = -0.3333333333 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667c + c2 = -0.3333333333 + 1.777777780

Combine like terms: -0.3333333333 + 1.777777780 = 1.4444444467
1.777777780 + -2.666666667c + c2 = 1.4444444467

Factor a perfect square on the left side:
(c + -1.333333334)(c + -1.333333334) = 1.4444444467

Calculate the square root of the right side: 1.201850426

Break this problem into two subproblems by setting 
(c + -1.333333334) equal to 1.201850426 and -1.201850426.


Subproblem 1
c + -1.333333334 = 1.201850426

Simplifying
c + -1.333333334 = 1.201850426

Reorder the terms:
-1.333333334 + c = 1.201850426

Solving
-1.333333334 + c = 1.201850426

Solving for variable 'c'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + c = 1.201850426 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + c = 1.201850426 + 1.333333334
c = 1.201850426 + 1.333333334

Combine like terms: 1.201850426 + 1.333333334 = 2.53518376
c = 2.53518376

Simplifying
c = 2.53518376


Subproblem 2
c + -1.333333334 = -1.201850426

Simplifying
c + -1.333333334 = -1.201850426

Reorder the terms:
-1.333333334 + c = -1.201850426

Solving
-1.333333334 + c = -1.201850426

Solving for variable 'c'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + c = -1.201850426 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + c = -1.201850426 + 1.333333334
c = -1.201850426 + 1.333333334

Combine like terms: -1.201850426 + 1.333333334 = 0.131482908
c = 0.131482908

Simplifying
c = 0.131482908


Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {2.53518376, 0.131482908}
Solution
c = {2.53518376, 0.131482908}

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