9*y^2-81*y-72=0

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Solution for 9*y^2-81*y-72=0 equation: 


Simplifying
9y2 + -81y + -72 = 0

Reorder the terms:
-72 + -81y + 9y2 = 0

Solving
-72 + -81y + 9y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '9'.
9(-8 + -9y + y2) = 0

Ignore the factor 9.

Subproblem 1
Set the factor '(-8 + -9y + y2)' equal to zero and attempt to solve:

Simplifying
-8 + -9y + y2 = 0

Solving
-8 + -9y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -9y + 8 + y2 = 0 + 8

Reorder the terms:
-8 + 8 + -9y + y2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -9y + y2 = 0 + 8
-9y + y2 = 0 + 8

Combine like terms: 0 + 8 = 8
-9y + y2 = 8

The y term is -9y.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9y + 20.25 + y2 = 8 + 20.25

Reorder the terms:
20.25 + -9y + y2 = 8 + 20.25

Combine like terms: 8 + 20.25 = 28.25
20.25 + -9y + y2 = 28.25

Factor a perfect square on the left side:
(y + -4.5)(y + -4.5) = 28.25

Calculate the square root of the right side: 5.315072906

Break this problem into two subproblems by setting 
(y + -4.5) equal to 5.315072906 and -5.315072906.


Subproblem 1
y + -4.5 = 5.315072906

Simplifying
y + -4.5 = 5.315072906

Reorder the terms:
-4.5 + y = 5.315072906

Solving
-4.5 + y = 5.315072906

Solving for variable 'y'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + y = 5.315072906 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + y = 5.315072906 + 4.5
y = 5.315072906 + 4.5

Combine like terms: 5.315072906 + 4.5 = 9.815072906
y = 9.815072906

Simplifying
y = 9.815072906


Subproblem 2
y + -4.5 = -5.315072906

Simplifying
y + -4.5 = -5.315072906

Reorder the terms:
-4.5 + y = -5.315072906

Solving
-4.5 + y = -5.315072906

Solving for variable 'y'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + y = -5.315072906 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + y = -5.315072906 + 4.5
y = -5.315072906 + 4.5

Combine like terms: -5.315072906 + 4.5 = -0.815072906
y = -0.815072906

Simplifying
y = -0.815072906


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {9.815072906, -0.815072906}
Solution
y = {9.815072906, -0.815072906}

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