12y^2-60y+62=0

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Solution for 12y^2-60y+62=0 equation: 


Simplifying
12y2 + -60y + 62 = 0

Reorder the terms:
62 + -60y + 12y2 = 0

Solving
62 + -60y + 12y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(31 + -30y + 6y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(31 + -30y + 6y2)' equal to zero and attempt to solve:

Simplifying
31 + -30y + 6y2 = 0

Solving
31 + -30y + 6y2 = 0

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

Divide each side by '6'.
5.166666667 + -5y + y2 = 0

Move the constant term to the right:

Add '-5.166666667' to each side of the equation.
5.166666667 + -5y + -5.166666667 + y2 = 0 + -5.166666667

Reorder the terms:
5.166666667 + -5.166666667 + -5y + y2 = 0 + -5.166666667

Combine like terms: 5.166666667 + -5.166666667 = 0.000000000
0.000000000 + -5y + y2 = 0 + -5.166666667
-5y + y2 = 0 + -5.166666667

Combine like terms: 0 + -5.166666667 = -5.166666667
-5y + y2 = -5.166666667

The y term is -5y.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5y + 6.25 + y2 = -5.166666667 + 6.25

Reorder the terms:
6.25 + -5y + y2 = -5.166666667 + 6.25

Combine like terms: -5.166666667 + 6.25 = 1.083333333
6.25 + -5y + y2 = 1.083333333

Factor a perfect square on the left side:
(y + -2.5)(y + -2.5) = 1.083333333

Calculate the square root of the right side: 1.040833

Break this problem into two subproblems by setting 
(y + -2.5) equal to 1.040833 and -1.040833.


Subproblem 1
y + -2.5 = 1.040833

Simplifying
y + -2.5 = 1.040833

Reorder the terms:
-2.5 + y = 1.040833

Solving
-2.5 + y = 1.040833

Solving for variable 'y'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + y = 1.040833 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + y = 1.040833 + 2.5
y = 1.040833 + 2.5

Combine like terms: 1.040833 + 2.5 = 3.540833
y = 3.540833

Simplifying
y = 3.540833


Subproblem 2
y + -2.5 = -1.040833

Simplifying
y + -2.5 = -1.040833

Reorder the terms:
-2.5 + y = -1.040833

Solving
-2.5 + y = -1.040833

Solving for variable 'y'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + y = -1.040833 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + y = -1.040833 + 2.5
y = -1.040833 + 2.5

Combine like terms: -1.040833 + 2.5 = 1.459167
y = 1.459167

Simplifying
y = 1.459167


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.540833, 1.459167}
Solution
y = {3.540833, 1.459167}

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