4x^2y+44xy-44y=0

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Solution for 4x^2y+44xy-44y=0 equation: 


Simplifying
4x2y + 44xy + -44y = 0

Reorder the terms:
44xy + 4x2y + -44y = 0

Solving
44xy + 4x2y + -44y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4y'.
4y(11x + x2 + -11) = 0

Ignore the factor 4.

Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Add '-1y' to each side of the equation.
y + -1y = 0 + -1y
Remove the zero:
0 = -1y

Simplifying
0 = -1y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(11x + x2 + -11)' equal to zero and attempt to solve:

Simplifying
11x + x2 + -11 = 0

Reorder the terms:
-11 + 11x + x2 = 0

Solving
-11 + 11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + 11x + 11 + x2 = 0 + 11

Reorder the terms:
-11 + 11 + 11x + x2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 11x + x2 = 0 + 11
11x + x2 = 0 + 11

Combine like terms: 0 + 11 = 11
11x + x2 = 11

The x term is 11x.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11x + 30.25 + x2 = 11 + 30.25

Reorder the terms:
30.25 + 11x + x2 = 11 + 30.25

Combine like terms: 11 + 30.25 = 41.25
30.25 + 11x + x2 = 41.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 41.25

Calculate the square root of the right side: 6.422616289

Break this problem into two subproblems by setting 
(x + 5.5) equal to 6.422616289 and -6.422616289.


Subproblem 1
x + 5.5 = 6.422616289

Simplifying
x + 5.5 = 6.422616289

Reorder the terms:
5.5 + x = 6.422616289

Solving
5.5 + x = 6.422616289

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = 6.422616289 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = 6.422616289 + -5.5
x = 6.422616289 + -5.5

Combine like terms: 6.422616289 + -5.5 = 0.922616289
x = 0.922616289

Simplifying
x = 0.922616289


Subproblem 2
x + 5.5 = -6.422616289

Simplifying
x + 5.5 = -6.422616289

Reorder the terms:
5.5 + x = -6.422616289

Solving
5.5 + x = -6.422616289

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = -6.422616289 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = -6.422616289 + -5.5
x = -6.422616289 + -5.5

Combine like terms: -6.422616289 + -5.5 = -11.922616289
x = -11.922616289

Simplifying
x = -11.922616289


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.922616289, -11.922616289}
Solution
x = {0.922616289, -11.922616289}

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