2x^2y+6xy-58y=0

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Solution for 2x^2y+6xy-58y=0 equation: 


Simplifying
2x2y + 6xy + -58y = 0

Reorder the terms:
6xy + 2x2y + -58y = 0

Solving
6xy + 2x2y + -58y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2y'.
2y(3x + x2 + -29) = 0

Ignore the factor 2.

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 '(3x + x2 + -29)' equal to zero and attempt to solve:

Simplifying
3x + x2 + -29 = 0

Reorder the terms:
-29 + 3x + x2 = 0

Solving
-29 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '29' to each side of the equation.
-29 + 3x + 29 + x2 = 0 + 29

Reorder the terms:
-29 + 29 + 3x + x2 = 0 + 29

Combine like terms: -29 + 29 = 0
0 + 3x + x2 = 0 + 29
3x + x2 = 0 + 29

Combine like terms: 0 + 29 = 29
3x + x2 = 29

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 29 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 29 + 2.25

Combine like terms: 29 + 2.25 = 31.25
2.25 + 3x + x2 = 31.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 31.25

Calculate the square root of the right side: 5.590169944

Break this problem into two subproblems by setting 
(x + 1.5) equal to 5.590169944 and -5.590169944.


Subproblem 1
x + 1.5 = 5.590169944

Simplifying
x + 1.5 = 5.590169944

Reorder the terms:
1.5 + x = 5.590169944

Solving
1.5 + x = 5.590169944

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 5.590169944 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 5.590169944 + -1.5
x = 5.590169944 + -1.5

Combine like terms: 5.590169944 + -1.5 = 4.090169944
x = 4.090169944

Simplifying
x = 4.090169944


Subproblem 2
x + 1.5 = -5.590169944

Simplifying
x + 1.5 = -5.590169944

Reorder the terms:
1.5 + x = -5.590169944

Solving
1.5 + x = -5.590169944

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -5.590169944 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -5.590169944 + -1.5
x = -5.590169944 + -1.5

Combine like terms: -5.590169944 + -1.5 = -7.090169944
x = -7.090169944

Simplifying
x = -7.090169944


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.090169944, -7.090169944}
Solution
x = {4.090169944, -7.090169944}

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