5x^2y+45xy-65y=0

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Solution for 5x^2y+45xy-65y=0 equation: 


Simplifying
5x2y + 45xy + -65y = 0

Reorder the terms:
45xy + 5x2y + -65y = 0

Solving
45xy + 5x2y + -65y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5y'.
5y(9x + x2 + -13) = 0

Ignore the factor 5.

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 '(9x + x2 + -13)' equal to zero and attempt to solve:

Simplifying
9x + x2 + -13 = 0

Reorder the terms:
-13 + 9x + x2 = 0

Solving
-13 + 9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + 9x + 13 + x2 = 0 + 13

Reorder the terms:
-13 + 13 + 9x + x2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + 9x + x2 = 0 + 13
9x + x2 = 0 + 13

Combine like terms: 0 + 13 = 13
9x + x2 = 13

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = 13 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 13 + 20.25

Combine like terms: 13 + 20.25 = 33.25
20.25 + 9x + x2 = 33.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 33.25

Calculate the square root of the right side: 5.766281297

Break this problem into two subproblems by setting 
(x + 4.5) equal to 5.766281297 and -5.766281297.


Subproblem 1
x + 4.5 = 5.766281297

Simplifying
x + 4.5 = 5.766281297

Reorder the terms:
4.5 + x = 5.766281297

Solving
4.5 + x = 5.766281297

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 5.766281297 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 5.766281297 + -4.5
x = 5.766281297 + -4.5

Combine like terms: 5.766281297 + -4.5 = 1.266281297
x = 1.266281297

Simplifying
x = 1.266281297


Subproblem 2
x + 4.5 = -5.766281297

Simplifying
x + 4.5 = -5.766281297

Reorder the terms:
4.5 + x = -5.766281297

Solving
4.5 + x = -5.766281297

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -5.766281297 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -5.766281297 + -4.5
x = -5.766281297 + -4.5

Combine like terms: -5.766281297 + -4.5 = -10.266281297
x = -10.266281297

Simplifying
x = -10.266281297


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.266281297, -10.266281297}
Solution
x = {1.266281297, -10.266281297}

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