3y^2+11y+4=0

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


Simplifying
3y2 + 11y + 4 = 0

Reorder the terms:
4 + 11y + 3y2 = 0

Solving
4 + 11y + 3y2 = 0

Solving for variable 'y'.

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

Divide each side by '3'.
1.333333333 + 3.666666667y + y2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + 3.666666667y + -1.333333333 + y2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + 3.666666667y + y2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + 3.666666667y + y2 = 0 + -1.333333333
3.666666667y + y2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
3.666666667y + y2 = -1.333333333

The y term is 3.666666667y.  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.
3.666666667y + 3.361111114 + y2 = -1.333333333 + 3.361111114

Reorder the terms:
3.361111114 + 3.666666667y + y2 = -1.333333333 + 3.361111114

Combine like terms: -1.333333333 + 3.361111114 = 2.027777781
3.361111114 + 3.666666667y + y2 = 2.027777781

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

Calculate the square root of the right side: 1.424000625

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


Subproblem 1
y + 1.833333334 = 1.424000625

Simplifying
y + 1.833333334 = 1.424000625

Reorder the terms:
1.833333334 + y = 1.424000625

Solving
1.833333334 + y = 1.424000625

Solving for variable 'y'.

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

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

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

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

Simplifying
y = -0.409332709


Subproblem 2
y + 1.833333334 = -1.424000625

Simplifying
y + 1.833333334 = -1.424000625

Reorder the terms:
1.833333334 + y = -1.424000625

Solving
1.833333334 + y = -1.424000625

Solving for variable 'y'.

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

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

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

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

Simplifying
y = -3.257333959


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

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