2y^2-66y-72=0

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Solution for 2y^2-66y-72=0 equation: 


Simplifying
2y2 + -66y + -72 = 0

Reorder the terms:
-72 + -66y + 2y2 = 0

Solving
-72 + -66y + 2y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-36 + -33y + y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-36 + -33y + y2)' equal to zero and attempt to solve:

Simplifying
-36 + -33y + y2 = 0

Solving
-36 + -33y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + -33y + 36 + y2 = 0 + 36

Reorder the terms:
-36 + 36 + -33y + y2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -33y + y2 = 0 + 36
-33y + y2 = 0 + 36

Combine like terms: 0 + 36 = 36
-33y + y2 = 36

The y term is -33y.  Take half its coefficient (-16.5).
Square it (272.25) and add it to both sides.

Add '272.25' to each side of the equation.
-33y + 272.25 + y2 = 36 + 272.25

Reorder the terms:
272.25 + -33y + y2 = 36 + 272.25

Combine like terms: 36 + 272.25 = 308.25
272.25 + -33y + y2 = 308.25

Factor a perfect square on the left side:
(y + -16.5)(y + -16.5) = 308.25

Calculate the square root of the right side: 17.557049866

Break this problem into two subproblems by setting 
(y + -16.5) equal to 17.557049866 and -17.557049866.


Subproblem 1
y + -16.5 = 17.557049866

Simplifying
y + -16.5 = 17.557049866

Reorder the terms:
-16.5 + y = 17.557049866

Solving
-16.5 + y = 17.557049866

Solving for variable 'y'.

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

Add '16.5' to each side of the equation.
-16.5 + 16.5 + y = 17.557049866 + 16.5

Combine like terms: -16.5 + 16.5 = 0.0
0.0 + y = 17.557049866 + 16.5
y = 17.557049866 + 16.5

Combine like terms: 17.557049866 + 16.5 = 34.057049866
y = 34.057049866

Simplifying
y = 34.057049866


Subproblem 2
y + -16.5 = -17.557049866

Simplifying
y + -16.5 = -17.557049866

Reorder the terms:
-16.5 + y = -17.557049866

Solving
-16.5 + y = -17.557049866

Solving for variable 'y'.

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

Add '16.5' to each side of the equation.
-16.5 + 16.5 + y = -17.557049866 + 16.5

Combine like terms: -16.5 + 16.5 = 0.0
0.0 + y = -17.557049866 + 16.5
y = -17.557049866 + 16.5

Combine like terms: -17.557049866 + 16.5 = -1.057049866
y = -1.057049866

Simplifying
y = -1.057049866


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {34.057049866, -1.057049866}
Solution
y = {34.057049866, -1.057049866}

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