5x^2y+25xy-65y=0

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Solution for 5x^2y+25xy-65y=0 equation: 


Simplifying
5x2y + 25xy + -65y = 0

Reorder the terms:
25xy + 5x2y + -65y = 0

Solving
25xy + 5x2y + -65y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5y'.
5y(5x + 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 '(5x + x2 + -13)' equal to zero and attempt to solve:

Simplifying
5x + x2 + -13 = 0

Reorder the terms:
-13 + 5x + x2 = 0

Solving
-13 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + 5x + 13 + x2 = 0 + 13

Reorder the terms:
-13 + 13 + 5x + x2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + 5x + x2 = 0 + 13
5x + x2 = 0 + 13

Combine like terms: 0 + 13 = 13
5x + x2 = 13

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 13 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 13 + 6.25

Combine like terms: 13 + 6.25 = 19.25
6.25 + 5x + x2 = 19.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 19.25

Calculate the square root of the right side: 4.387482194

Break this problem into two subproblems by setting 
(x + 2.5) equal to 4.387482194 and -4.387482194.


Subproblem 1
x + 2.5 = 4.387482194

Simplifying
x + 2.5 = 4.387482194

Reorder the terms:
2.5 + x = 4.387482194

Solving
2.5 + x = 4.387482194

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 4.387482194 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 4.387482194 + -2.5
x = 4.387482194 + -2.5

Combine like terms: 4.387482194 + -2.5 = 1.887482194
x = 1.887482194

Simplifying
x = 1.887482194


Subproblem 2
x + 2.5 = -4.387482194

Simplifying
x + 2.5 = -4.387482194

Reorder the terms:
2.5 + x = -4.387482194

Solving
2.5 + x = -4.387482194

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -4.387482194 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -4.387482194 + -2.5
x = -4.387482194 + -2.5

Combine like terms: -4.387482194 + -2.5 = -6.887482194
x = -6.887482194

Simplifying
x = -6.887482194


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.887482194, -6.887482194}
Solution
x = {1.887482194, -6.887482194}

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