-2y^2+33y-27=0

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Solution for -2y^2+33y-27=0 equation: 


Simplifying
-2y2 + 33y + -27 = 0

Reorder the terms:
-27 + 33y + -2y2 = 0

Solving
-27 + 33y + -2y2 = 0

Solving for variable 'y'.

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
13.5 + -16.5y + y2 = 0

Move the constant term to the right:

Add '-13.5' to each side of the equation.
13.5 + -16.5y + -13.5 + y2 = 0 + -13.5

Reorder the terms:
13.5 + -13.5 + -16.5y + y2 = 0 + -13.5

Combine like terms: 13.5 + -13.5 = 0.0
0.0 + -16.5y + y2 = 0 + -13.5
-16.5y + y2 = 0 + -13.5

Combine like terms: 0 + -13.5 = -13.5
-16.5y + y2 = -13.5

The y term is -16.5y.  Take half its coefficient (-8.25).
Square it (68.0625) and add it to both sides.

Add '68.0625' to each side of the equation.
-16.5y + 68.0625 + y2 = -13.5 + 68.0625

Reorder the terms:
68.0625 + -16.5y + y2 = -13.5 + 68.0625

Combine like terms: -13.5 + 68.0625 = 54.5625
68.0625 + -16.5y + y2 = 54.5625

Factor a perfect square on the left side:
(y + -8.25)(y + -8.25) = 54.5625

Calculate the square root of the right side: 7.386643351

Break this problem into two subproblems by setting 
(y + -8.25) equal to 7.386643351 and -7.386643351.


Subproblem 1
y + -8.25 = 7.386643351

Simplifying
y + -8.25 = 7.386643351

Reorder the terms:
-8.25 + y = 7.386643351

Solving
-8.25 + y = 7.386643351

Solving for variable 'y'.

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

Add '8.25' to each side of the equation.
-8.25 + 8.25 + y = 7.386643351 + 8.25

Combine like terms: -8.25 + 8.25 = 0.00
0.00 + y = 7.386643351 + 8.25
y = 7.386643351 + 8.25

Combine like terms: 7.386643351 + 8.25 = 15.636643351
y = 15.636643351

Simplifying
y = 15.636643351


Subproblem 2
y + -8.25 = -7.386643351

Simplifying
y + -8.25 = -7.386643351

Reorder the terms:
-8.25 + y = -7.386643351

Solving
-8.25 + y = -7.386643351

Solving for variable 'y'.

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

Add '8.25' to each side of the equation.
-8.25 + 8.25 + y = -7.386643351 + 8.25

Combine like terms: -8.25 + 8.25 = 0.00
0.00 + y = -7.386643351 + 8.25
y = -7.386643351 + 8.25

Combine like terms: -7.386643351 + 8.25 = 0.863356649
y = 0.863356649

Simplifying
y = 0.863356649


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {15.636643351, 0.863356649}

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