6c^2-34c+18=0

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Solution for 6c^2-34c+18=0 equation: 


Simplifying
6c2 + -34c + 18 = 0

Reorder the terms:
18 + -34c + 6c2 = 0

Solving
18 + -34c + 6c2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + -17c + 3c2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(9 + -17c + 3c2)' equal to zero and attempt to solve:

Simplifying
9 + -17c + 3c2 = 0

Solving
9 + -17c + 3c2 = 0

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

Divide each side by '3'.
3 + -5.666666667c + c2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -5.666666667c + -3 + c2 = 0 + -3

Reorder the terms:
3 + -3 + -5.666666667c + c2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5.666666667c + c2 = 0 + -3
-5.666666667c + c2 = 0 + -3

Combine like terms: 0 + -3 = -3
-5.666666667c + c2 = -3

The c term is -5.666666667c.  Take half its coefficient (-2.833333334).
Square it (8.027777782) and add it to both sides.

Add '8.027777782' to each side of the equation.
-5.666666667c + 8.027777782 + c2 = -3 + 8.027777782

Reorder the terms:
8.027777782 + -5.666666667c + c2 = -3 + 8.027777782

Combine like terms: -3 + 8.027777782 = 5.027777782
8.027777782 + -5.666666667c + c2 = 5.027777782

Factor a perfect square on the left side:
(c + -2.833333334)(c + -2.833333334) = 5.027777782

Calculate the square root of the right side: 2.242270675

Break this problem into two subproblems by setting 
(c + -2.833333334) equal to 2.242270675 and -2.242270675.


Subproblem 1
c + -2.833333334 = 2.242270675

Simplifying
c + -2.833333334 = 2.242270675

Reorder the terms:
-2.833333334 + c = 2.242270675

Solving
-2.833333334 + c = 2.242270675

Solving for variable 'c'.

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

Add '2.833333334' to each side of the equation.
-2.833333334 + 2.833333334 + c = 2.242270675 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + c = 2.242270675 + 2.833333334
c = 2.242270675 + 2.833333334

Combine like terms: 2.242270675 + 2.833333334 = 5.075604009
c = 5.075604009

Simplifying
c = 5.075604009


Subproblem 2
c + -2.833333334 = -2.242270675

Simplifying
c + -2.833333334 = -2.242270675

Reorder the terms:
-2.833333334 + c = -2.242270675

Solving
-2.833333334 + c = -2.242270675

Solving for variable 'c'.

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

Add '2.833333334' to each side of the equation.
-2.833333334 + 2.833333334 + c = -2.242270675 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + c = -2.242270675 + 2.833333334
c = -2.242270675 + 2.833333334

Combine like terms: -2.242270675 + 2.833333334 = 0.591062659
c = 0.591062659

Simplifying
c = 0.591062659


Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {5.075604009, 0.591062659}
Solution
c = {5.075604009, 0.591062659}

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