2x^2y+4xy-58y=0

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Solution for 2x^2y+4xy-58y=0 equation: 


Simplifying
2x2y + 4xy + -58y = 0

Reorder the terms:
4xy + 2x2y + -58y = 0

Solving
4xy + 2x2y + -58y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2y'.
2y(2x + 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 '(2x + x2 + -29)' equal to zero and attempt to solve:

Simplifying
2x + x2 + -29 = 0

Reorder the terms:
-29 + 2x + x2 = 0

Solving
-29 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '29' to each side of the equation.
-29 + 2x + 29 + x2 = 0 + 29

Reorder the terms:
-29 + 29 + 2x + x2 = 0 + 29

Combine like terms: -29 + 29 = 0
0 + 2x + x2 = 0 + 29
2x + x2 = 0 + 29

Combine like terms: 0 + 29 = 29
2x + x2 = 29

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 29 + 1

Reorder the terms:
1 + 2x + x2 = 29 + 1

Combine like terms: 29 + 1 = 30
1 + 2x + x2 = 30

Factor a perfect square on the left side:
(x + 1)(x + 1) = 30

Calculate the square root of the right side: 5.477225575

Break this problem into two subproblems by setting 
(x + 1) equal to 5.477225575 and -5.477225575.


Subproblem 1
x + 1 = 5.477225575

Simplifying
x + 1 = 5.477225575

Reorder the terms:
1 + x = 5.477225575

Solving
1 + x = 5.477225575

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 5.477225575 + -1

Combine like terms: 1 + -1 = 0
0 + x = 5.477225575 + -1
x = 5.477225575 + -1

Combine like terms: 5.477225575 + -1 = 4.477225575
x = 4.477225575

Simplifying
x = 4.477225575


Subproblem 2
x + 1 = -5.477225575

Simplifying
x + 1 = -5.477225575

Reorder the terms:
1 + x = -5.477225575

Solving
1 + x = -5.477225575

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -5.477225575 + -1

Combine like terms: 1 + -1 = 0
0 + x = -5.477225575 + -1
x = -5.477225575 + -1

Combine like terms: -5.477225575 + -1 = -6.477225575
x = -6.477225575

Simplifying
x = -6.477225575


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.477225575, -6.477225575}
Solution
x = {4.477225575, -6.477225575}

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