3y^2+44y-14=0

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Solution for 3y^2+44y-14=0 equation: 


Simplifying
3y2 + 44y + -14 = 0

Reorder the terms:
-14 + 44y + 3y2 = 0

Solving
-14 + 44y + 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'.
-4.666666667 + 14.66666667y + y2 = 0

Move the constant term to the right:

Add '4.666666667' to each side of the equation.
-4.666666667 + 14.66666667y + 4.666666667 + y2 = 0 + 4.666666667

Reorder the terms:
-4.666666667 + 4.666666667 + 14.66666667y + y2 = 0 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + 14.66666667y + y2 = 0 + 4.666666667
14.66666667y + y2 = 0 + 4.666666667

Combine like terms: 0 + 4.666666667 = 4.666666667
14.66666667y + y2 = 4.666666667

The y term is 14.66666667y.  Take half its coefficient (7.333333335).
Square it (53.77777780) and add it to both sides.

Add '53.77777780' to each side of the equation.
14.66666667y + 53.77777780 + y2 = 4.666666667 + 53.77777780

Reorder the terms:
53.77777780 + 14.66666667y + y2 = 4.666666667 + 53.77777780

Combine like terms: 4.666666667 + 53.77777780 = 58.444444467
53.77777780 + 14.66666667y + y2 = 58.444444467

Factor a perfect square on the left side:
(y + 7.333333335)(y + 7.333333335) = 58.444444467

Calculate the square root of the right side: 7.644896629

Break this problem into two subproblems by setting 
(y + 7.333333335) equal to 7.644896629 and -7.644896629.


Subproblem 1
y + 7.333333335 = 7.644896629

Simplifying
y + 7.333333335 = 7.644896629

Reorder the terms:
7.333333335 + y = 7.644896629

Solving
7.333333335 + y = 7.644896629

Solving for variable 'y'.

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

Add '-7.333333335' to each side of the equation.
7.333333335 + -7.333333335 + y = 7.644896629 + -7.333333335

Combine like terms: 7.333333335 + -7.333333335 = 0.000000000
0.000000000 + y = 7.644896629 + -7.333333335
y = 7.644896629 + -7.333333335

Combine like terms: 7.644896629 + -7.333333335 = 0.311563294
y = 0.311563294

Simplifying
y = 0.311563294


Subproblem 2
y + 7.333333335 = -7.644896629

Simplifying
y + 7.333333335 = -7.644896629

Reorder the terms:
7.333333335 + y = -7.644896629

Solving
7.333333335 + y = -7.644896629

Solving for variable 'y'.

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

Add '-7.333333335' to each side of the equation.
7.333333335 + -7.333333335 + y = -7.644896629 + -7.333333335

Combine like terms: 7.333333335 + -7.333333335 = 0.000000000
0.000000000 + y = -7.644896629 + -7.333333335
y = -7.644896629 + -7.333333335

Combine like terms: -7.644896629 + -7.333333335 = -14.978229964
y = -14.978229964

Simplifying
y = -14.978229964


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.311563294, -14.978229964}

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