12y^2+29y=15

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Solution for 12y^2+29y=15 equation:


Simplifying
12y2 + 29y = 15

Reorder the terms:
29y + 12y2 = 15

Solving
29y + 12y2 = 15

Solving for variable 'y'.

Reorder the terms:
-15 + 29y + 12y2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + 29y + 12y2 = 0

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

Divide each side by '12'.
-1.25 + 2.416666667y + y2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + 2.416666667y + 1.25 + y2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + 2.416666667y + y2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + 2.416666667y + y2 = 0 + 1.25
2.416666667y + y2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
2.416666667y + y2 = 1.25

The y term is 2.416666667y.  Take half its coefficient (1.208333334).
Square it (1.460069446) and add it to both sides.

Add '1.460069446' to each side of the equation.
2.416666667y + 1.460069446 + y2 = 1.25 + 1.460069446

Reorder the terms:
1.460069446 + 2.416666667y + y2 = 1.25 + 1.460069446

Combine like terms: 1.25 + 1.460069446 = 2.710069446
1.460069446 + 2.416666667y + y2 = 2.710069446

Factor a perfect square on the left side:
(y + 1.208333334)(y + 1.208333334) = 2.710069446

Calculate the square root of the right side: 1.646228856

Break this problem into two subproblems by setting 
(y + 1.208333334) equal to 1.646228856 and -1.646228856.

Subproblem 1

y + 1.208333334 = 1.646228856 Simplifying y + 1.208333334 = 1.646228856 Reorder the terms: 1.208333334 + y = 1.646228856 Solving 1.208333334 + y = 1.646228856 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.208333334' to each side of the equation. 1.208333334 + -1.208333334 + y = 1.646228856 + -1.208333334 Combine like terms: 1.208333334 + -1.208333334 = 0.000000000 0.000000000 + y = 1.646228856 + -1.208333334 y = 1.646228856 + -1.208333334 Combine like terms: 1.646228856 + -1.208333334 = 0.437895522 y = 0.437895522 Simplifying y = 0.437895522

Subproblem 2

y + 1.208333334 = -1.646228856 Simplifying y + 1.208333334 = -1.646228856 Reorder the terms: 1.208333334 + y = -1.646228856 Solving 1.208333334 + y = -1.646228856 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.208333334' to each side of the equation. 1.208333334 + -1.208333334 + y = -1.646228856 + -1.208333334 Combine like terms: 1.208333334 + -1.208333334 = 0.000000000 0.000000000 + y = -1.646228856 + -1.208333334 y = -1.646228856 + -1.208333334 Combine like terms: -1.646228856 + -1.208333334 = -2.85456219 y = -2.85456219 Simplifying y = -2.85456219

Solution

The solution to the problem is based on the solutions from the subproblems. y = {0.437895522, -2.85456219}

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