9y^2-60y+88=0

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Solution for 9y^2-60y+88=0 equation: 


Simplifying
9y2 + -60y + 88 = 0

Reorder the terms:
88 + -60y + 9y2 = 0

Solving
88 + -60y + 9y2 = 0

Solving for variable 'y'.

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

Divide each side by '9'.
9.777777778 + -6.666666667y + y2 = 0

Move the constant term to the right:

Add '-9.777777778' to each side of the equation.
9.777777778 + -6.666666667y + -9.777777778 + y2 = 0 + -9.777777778

Reorder the terms:
9.777777778 + -9.777777778 + -6.666666667y + y2 = 0 + -9.777777778

Combine like terms: 9.777777778 + -9.777777778 = 0.000000000
0.000000000 + -6.666666667y + y2 = 0 + -9.777777778
-6.666666667y + y2 = 0 + -9.777777778

Combine like terms: 0 + -9.777777778 = -9.777777778
-6.666666667y + y2 = -9.777777778

The y term is -6.666666667y.  Take half its coefficient (-3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
-6.666666667y + 11.11111112 + y2 = -9.777777778 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667y + y2 = -9.777777778 + 11.11111112

Combine like terms: -9.777777778 + 11.11111112 = 1.333333342
11.11111112 + -6.666666667y + y2 = 1.333333342

Factor a perfect square on the left side:
(y + -3.333333334)(y + -3.333333334) = 1.333333342

Calculate the square root of the right side: 1.154700542

Break this problem into two subproblems by setting 
(y + -3.333333334) equal to 1.154700542 and -1.154700542.


Subproblem 1
y + -3.333333334 = 1.154700542

Simplifying
y + -3.333333334 = 1.154700542

Reorder the terms:
-3.333333334 + y = 1.154700542

Solving
-3.333333334 + y = 1.154700542

Solving for variable 'y'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + y = 1.154700542 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + y = 1.154700542 + 3.333333334
y = 1.154700542 + 3.333333334

Combine like terms: 1.154700542 + 3.333333334 = 4.488033876
y = 4.488033876

Simplifying
y = 4.488033876


Subproblem 2
y + -3.333333334 = -1.154700542

Simplifying
y + -3.333333334 = -1.154700542

Reorder the terms:
-3.333333334 + y = -1.154700542

Solving
-3.333333334 + y = -1.154700542

Solving for variable 'y'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + y = -1.154700542 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + y = -1.154700542 + 3.333333334
y = -1.154700542 + 3.333333334

Combine like terms: -1.154700542 + 3.333333334 = 2.178632792
y = 2.178632792

Simplifying
y = 2.178632792


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.488033876, 2.178632792}

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