12y^2+11y-34=0

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Solution for 12y^2+11y-34=0 equation: 


Simplifying
12y2 + 11y + -34 = 0

Reorder the terms:
-34 + 11y + 12y2 = 0

Solving
-34 + 11y + 12y2 = 0

Solving for variable 'y'.

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

Divide each side by '12'.
-2.833333333 + 0.9166666667y + y2 = 0

Move the constant term to the right:

Add '2.833333333' to each side of the equation.
-2.833333333 + 0.9166666667y + 2.833333333 + y2 = 0 + 2.833333333

Reorder the terms:
-2.833333333 + 2.833333333 + 0.9166666667y + y2 = 0 + 2.833333333

Combine like terms: -2.833333333 + 2.833333333 = 0.000000000
0.000000000 + 0.9166666667y + y2 = 0 + 2.833333333
0.9166666667y + y2 = 0 + 2.833333333

Combine like terms: 0 + 2.833333333 = 2.833333333
0.9166666667y + y2 = 2.833333333

The y term is 0.9166666667y.  Take half its coefficient (0.4583333334).
Square it (0.2100694445) and add it to both sides.

Add '0.2100694445' to each side of the equation.
0.9166666667y + 0.2100694445 + y2 = 2.833333333 + 0.2100694445

Reorder the terms:
0.2100694445 + 0.9166666667y + y2 = 2.833333333 + 0.2100694445

Combine like terms: 2.833333333 + 0.2100694445 = 3.0434027775
0.2100694445 + 0.9166666667y + y2 = 3.0434027775

Factor a perfect square on the left side:
(y + 0.4583333334)(y + 0.4583333334) = 3.0434027775

Calculate the square root of the right side: 1.744535118

Break this problem into two subproblems by setting 
(y + 0.4583333334) equal to 1.744535118 and -1.744535118.


Subproblem 1
y + 0.4583333334 = 1.744535118

Simplifying
y + 0.4583333334 = 1.744535118

Reorder the terms:
0.4583333334 + y = 1.744535118

Solving
0.4583333334 + y = 1.744535118

Solving for variable 'y'.

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

Add '-0.4583333334' to each side of the equation.
0.4583333334 + -0.4583333334 + y = 1.744535118 + -0.4583333334

Combine like terms: 0.4583333334 + -0.4583333334 = 0.0000000000
0.0000000000 + y = 1.744535118 + -0.4583333334
y = 1.744535118 + -0.4583333334

Combine like terms: 1.744535118 + -0.4583333334 = 1.2862017846
y = 1.2862017846

Simplifying
y = 1.2862017846


Subproblem 2
y + 0.4583333334 = -1.744535118

Simplifying
y + 0.4583333334 = -1.744535118

Reorder the terms:
0.4583333334 + y = -1.744535118

Solving
0.4583333334 + y = -1.744535118

Solving for variable 'y'.

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

Add '-0.4583333334' to each side of the equation.
0.4583333334 + -0.4583333334 + y = -1.744535118 + -0.4583333334

Combine like terms: 0.4583333334 + -0.4583333334 = 0.0000000000
0.0000000000 + y = -1.744535118 + -0.4583333334
y = -1.744535118 + -0.4583333334

Combine like terms: -1.744535118 + -0.4583333334 = -2.2028684514
y = -2.2028684514

Simplifying
y = -2.2028684514


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.2862017846, -2.2028684514}

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