6y^2-29y+5=0

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Solution for 6y^2-29y+5=0 equation: 


Simplifying
6y2 + -29y + 5 = 0

Reorder the terms:
5 + -29y + 6y2 = 0

Solving
5 + -29y + 6y2 = 0

Solving for variable 'y'.

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

Divide each side by '6'.
0.8333333333 + -4.833333333y + y2 = 0

Move the constant term to the right:

Add '-0.8333333333' to each side of the equation.
0.8333333333 + -4.833333333y + -0.8333333333 + y2 = 0 + -0.8333333333

Reorder the terms:
0.8333333333 + -0.8333333333 + -4.833333333y + y2 = 0 + -0.8333333333

Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000
0.0000000000 + -4.833333333y + y2 = 0 + -0.8333333333
-4.833333333y + y2 = 0 + -0.8333333333

Combine like terms: 0 + -0.8333333333 = -0.8333333333
-4.833333333y + y2 = -0.8333333333

The y term is -4.833333333y.  Take half its coefficient (-2.416666667).
Square it (5.840277779) and add it to both sides.

Add '5.840277779' to each side of the equation.
-4.833333333y + 5.840277779 + y2 = -0.8333333333 + 5.840277779

Reorder the terms:
5.840277779 + -4.833333333y + y2 = -0.8333333333 + 5.840277779

Combine like terms: -0.8333333333 + 5.840277779 = 5.0069444457
5.840277779 + -4.833333333y + y2 = 5.0069444457

Factor a perfect square on the left side:
(y + -2.416666667)(y + -2.416666667) = 5.0069444457

Calculate the square root of the right side: 2.237620264

Break this problem into two subproblems by setting 
(y + -2.416666667) equal to 2.237620264 and -2.237620264.


Subproblem 1
y + -2.416666667 = 2.237620264

Simplifying
y + -2.416666667 = 2.237620264

Reorder the terms:
-2.416666667 + y = 2.237620264

Solving
-2.416666667 + y = 2.237620264

Solving for variable 'y'.

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

Add '2.416666667' to each side of the equation.
-2.416666667 + 2.416666667 + y = 2.237620264 + 2.416666667

Combine like terms: -2.416666667 + 2.416666667 = 0.000000000
0.000000000 + y = 2.237620264 + 2.416666667
y = 2.237620264 + 2.416666667

Combine like terms: 2.237620264 + 2.416666667 = 4.654286931
y = 4.654286931

Simplifying
y = 4.654286931


Subproblem 2
y + -2.416666667 = -2.237620264

Simplifying
y + -2.416666667 = -2.237620264

Reorder the terms:
-2.416666667 + y = -2.237620264

Solving
-2.416666667 + y = -2.237620264

Solving for variable 'y'.

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

Add '2.416666667' to each side of the equation.
-2.416666667 + 2.416666667 + y = -2.237620264 + 2.416666667

Combine like terms: -2.416666667 + 2.416666667 = 0.000000000
0.000000000 + y = -2.237620264 + 2.416666667
y = -2.237620264 + 2.416666667

Combine like terms: -2.237620264 + 2.416666667 = 0.179046403
y = 0.179046403

Simplifying
y = 0.179046403


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.654286931, 0.179046403}

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