3c^2-17c+16=

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Solution for 3c^2-17c+16= equation: 


Simplifying
3c2 + -17c + 16 = 0

Reorder the terms:
16 + -17c + 3c2 = 0

Solving
16 + -17c + 3c2 = 0

Solving for variable 'c'.

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

Divide each side by '3'.
5.333333333 + -5.666666667c + c2 = 0

Move the constant term to the right:

Add '-5.333333333' to each side of the equation.
5.333333333 + -5.666666667c + -5.333333333 + c2 = 0 + -5.333333333

Reorder the terms:
5.333333333 + -5.333333333 + -5.666666667c + c2 = 0 + -5.333333333

Combine like terms: 5.333333333 + -5.333333333 = 0.000000000
0.000000000 + -5.666666667c + c2 = 0 + -5.333333333
-5.666666667c + c2 = 0 + -5.333333333

Combine like terms: 0 + -5.333333333 = -5.333333333
-5.666666667c + c2 = -5.333333333

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 = -5.333333333 + 8.027777782

Reorder the terms:
8.027777782 + -5.666666667c + c2 = -5.333333333 + 8.027777782

Combine like terms: -5.333333333 + 8.027777782 = 2.694444449
8.027777782 + -5.666666667c + c2 = 2.694444449

Factor a perfect square on the left side:
(c + -2.833333334)(c + -2.833333334) = 2.694444449

Calculate the square root of the right side: 1.641476302

Break this problem into two subproblems by setting 
(c + -2.833333334) equal to 1.641476302 and -1.641476302.


Subproblem 1
c + -2.833333334 = 1.641476302

Simplifying
c + -2.833333334 = 1.641476302

Reorder the terms:
-2.833333334 + c = 1.641476302

Solving
-2.833333334 + c = 1.641476302

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 = 1.641476302 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + c = 1.641476302 + 2.833333334
c = 1.641476302 + 2.833333334

Combine like terms: 1.641476302 + 2.833333334 = 4.474809636
c = 4.474809636

Simplifying
c = 4.474809636


Subproblem 2
c + -2.833333334 = -1.641476302

Simplifying
c + -2.833333334 = -1.641476302

Reorder the terms:
-2.833333334 + c = -1.641476302

Solving
-2.833333334 + c = -1.641476302

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 = -1.641476302 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + c = -1.641476302 + 2.833333334
c = -1.641476302 + 2.833333334

Combine like terms: -1.641476302 + 2.833333334 = 1.191857032
c = 1.191857032

Simplifying
c = 1.191857032


Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {4.474809636, 1.191857032}

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