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 = 13.361111115
8.027777782 + -5.666666667c + c2 = 13.361111115

Factor a perfect square on the left side:
(c + -2.833333334)(c + -2.833333334) = 13.361111115

Calculate the square root of the right side: 3.655285367

Break this problem into two subproblems by setting 
(c + -2.833333334) equal to 3.655285367 and -3.655285367.


Subproblem 1
c + -2.833333334 = 3.655285367

Simplifying
c + -2.833333334 = 3.655285367

Reorder the terms:
-2.833333334 + c = 3.655285367

Solving
-2.833333334 + c = 3.655285367

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 = 3.655285367 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + c = 3.655285367 + 2.833333334
c = 3.655285367 + 2.833333334

Combine like terms: 3.655285367 + 2.833333334 = 6.488618701
c = 6.488618701

Simplifying
c = 6.488618701


Subproblem 2
c + -2.833333334 = -3.655285367

Simplifying
c + -2.833333334 = -3.655285367

Reorder the terms:
-2.833333334 + c = -3.655285367

Solving
-2.833333334 + c = -3.655285367

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 = -3.655285367 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + c = -3.655285367 + 2.833333334
c = -3.655285367 + 2.833333334

Combine like terms: -3.655285367 + 2.833333334 = -0.821952033
c = -0.821952033

Simplifying
c = -0.821952033


Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {6.488618701, -0.821952033}

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