3c^2+11c+4=0

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Solution for 3c^2+11c+4=0 equation: 


Simplifying
3c2 + 11c + 4 = 0

Reorder the terms:
4 + 11c + 3c2 = 0

Solving
4 + 11c + 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'.
1.333333333 + 3.666666667c + c2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + 3.666666667c + -1.333333333 + c2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + 3.666666667c + c2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + 3.666666667c + c2 = 0 + -1.333333333
3.666666667c + c2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
3.666666667c + c2 = -1.333333333

The c term is 3.666666667c.  Take half its coefficient (1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
3.666666667c + 3.361111114 + c2 = -1.333333333 + 3.361111114

Reorder the terms:
3.361111114 + 3.666666667c + c2 = -1.333333333 + 3.361111114

Combine like terms: -1.333333333 + 3.361111114 = 2.027777781
3.361111114 + 3.666666667c + c2 = 2.027777781

Factor a perfect square on the left side:
(c + 1.833333334)(c + 1.833333334) = 2.027777781

Calculate the square root of the right side: 1.424000625

Break this problem into two subproblems by setting 
(c + 1.833333334) equal to 1.424000625 and -1.424000625.


Subproblem 1
c + 1.833333334 = 1.424000625

Simplifying
c + 1.833333334 = 1.424000625

Reorder the terms:
1.833333334 + c = 1.424000625

Solving
1.833333334 + c = 1.424000625

Solving for variable 'c'.

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

Add '-1.833333334' to each side of the equation.
1.833333334 + -1.833333334 + c = 1.424000625 + -1.833333334

Combine like terms: 1.833333334 + -1.833333334 = 0.000000000
0.000000000 + c = 1.424000625 + -1.833333334
c = 1.424000625 + -1.833333334

Combine like terms: 1.424000625 + -1.833333334 = -0.409332709
c = -0.409332709

Simplifying
c = -0.409332709


Subproblem 2
c + 1.833333334 = -1.424000625

Simplifying
c + 1.833333334 = -1.424000625

Reorder the terms:
1.833333334 + c = -1.424000625

Solving
1.833333334 + c = -1.424000625

Solving for variable 'c'.

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

Add '-1.833333334' to each side of the equation.
1.833333334 + -1.833333334 + c = -1.424000625 + -1.833333334

Combine like terms: 1.833333334 + -1.833333334 = 0.000000000
0.000000000 + c = -1.424000625 + -1.833333334
c = -1.424000625 + -1.833333334

Combine like terms: -1.424000625 + -1.833333334 = -3.257333959
c = -3.257333959

Simplifying
c = -3.257333959


Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {-0.409332709, -3.257333959}

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