2x^2y+24xy-58y=0

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Solution for 2x^2y+24xy-58y=0 equation: 


Simplifying
2x2y + 24xy + -58y = 0

Reorder the terms:
24xy + 2x2y + -58y = 0

Solving
24xy + 2x2y + -58y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2y'.
2y(12x + 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 '(12x + x2 + -29)' equal to zero and attempt to solve:

Simplifying
12x + x2 + -29 = 0

Reorder the terms:
-29 + 12x + x2 = 0

Solving
-29 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '29' to each side of the equation.
-29 + 12x + 29 + x2 = 0 + 29

Reorder the terms:
-29 + 29 + 12x + x2 = 0 + 29

Combine like terms: -29 + 29 = 0
0 + 12x + x2 = 0 + 29
12x + x2 = 0 + 29

Combine like terms: 0 + 29 = 29
12x + x2 = 29

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 29 + 36

Reorder the terms:
36 + 12x + x2 = 29 + 36

Combine like terms: 29 + 36 = 65
36 + 12x + x2 = 65

Factor a perfect square on the left side:
(x + 6)(x + 6) = 65

Calculate the square root of the right side: 8.062257748

Break this problem into two subproblems by setting 
(x + 6) equal to 8.062257748 and -8.062257748.


Subproblem 1
x + 6 = 8.062257748

Simplifying
x + 6 = 8.062257748

Reorder the terms:
6 + x = 8.062257748

Solving
6 + x = 8.062257748

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = 8.062257748 + -6

Combine like terms: 6 + -6 = 0
0 + x = 8.062257748 + -6
x = 8.062257748 + -6

Combine like terms: 8.062257748 + -6 = 2.062257748
x = 2.062257748

Simplifying
x = 2.062257748


Subproblem 2
x + 6 = -8.062257748

Simplifying
x + 6 = -8.062257748

Reorder the terms:
6 + x = -8.062257748

Solving
6 + x = -8.062257748

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = -8.062257748 + -6

Combine like terms: 6 + -6 = 0
0 + x = -8.062257748 + -6
x = -8.062257748 + -6

Combine like terms: -8.062257748 + -6 = -14.062257748
x = -14.062257748

Simplifying
x = -14.062257748


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.062257748, -14.062257748}
Solution
x = {2.062257748, -14.062257748}

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