4x^2y+52xy-92y=0

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Solution for 4x^2y+52xy-92y=0 equation: 


Simplifying
4x2y + 52xy + -92y = 0

Reorder the terms:
52xy + 4x2y + -92y = 0

Solving
52xy + 4x2y + -92y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4y'.
4y(13x + x2 + -23) = 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 '(13x + x2 + -23)' equal to zero and attempt to solve:

Simplifying
13x + x2 + -23 = 0

Reorder the terms:
-23 + 13x + x2 = 0

Solving
-23 + 13x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '23' to each side of the equation.
-23 + 13x + 23 + x2 = 0 + 23

Reorder the terms:
-23 + 23 + 13x + x2 = 0 + 23

Combine like terms: -23 + 23 = 0
0 + 13x + x2 = 0 + 23
13x + x2 = 0 + 23

Combine like terms: 0 + 23 = 23
13x + x2 = 23

The x term is 13x.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13x + 42.25 + x2 = 23 + 42.25

Reorder the terms:
42.25 + 13x + x2 = 23 + 42.25

Combine like terms: 23 + 42.25 = 65.25
42.25 + 13x + x2 = 65.25

Factor a perfect square on the left side:
(x + 6.5)(x + 6.5) = 65.25

Calculate the square root of the right side: 8.077747211

Break this problem into two subproblems by setting 
(x + 6.5) equal to 8.077747211 and -8.077747211.


Subproblem 1
x + 6.5 = 8.077747211

Simplifying
x + 6.5 = 8.077747211

Reorder the terms:
6.5 + x = 8.077747211

Solving
6.5 + x = 8.077747211

Solving for variable 'x'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + x = 8.077747211 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = 8.077747211 + -6.5
x = 8.077747211 + -6.5

Combine like terms: 8.077747211 + -6.5 = 1.577747211
x = 1.577747211

Simplifying
x = 1.577747211


Subproblem 2
x + 6.5 = -8.077747211

Simplifying
x + 6.5 = -8.077747211

Reorder the terms:
6.5 + x = -8.077747211

Solving
6.5 + x = -8.077747211

Solving for variable 'x'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + x = -8.077747211 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = -8.077747211 + -6.5
x = -8.077747211 + -6.5

Combine like terms: -8.077747211 + -6.5 = -14.577747211
x = -14.577747211

Simplifying
x = -14.577747211


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.577747211, -14.577747211}
Solution
x = {1.577747211, -14.577747211}

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