2x^2y+16xy-4y=

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Solution for 2x^2y+16xy-4y= equation: 


Simplifying
2x2y + 16xy + -4y = 0

Reorder the terms:
16xy + 2x2y + -4y = 0

Solving
16xy + 2x2y + -4y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2y'.
2y(8x + x2 + -2) = 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 '(8x + x2 + -2)' equal to zero and attempt to solve:

Simplifying
8x + x2 + -2 = 0

Reorder the terms:
-2 + 8x + x2 = 0

Solving
-2 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 8x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 8x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 8x + x2 = 0 + 2
8x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
8x + x2 = 2

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 2 + 16

Reorder the terms:
16 + 8x + x2 = 2 + 16

Combine like terms: 2 + 16 = 18
16 + 8x + x2 = 18

Factor a perfect square on the left side:
(x + 4)(x + 4) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(x + 4) equal to 4.242640687 and -4.242640687.


Subproblem 1
x + 4 = 4.242640687

Simplifying
x + 4 = 4.242640687

Reorder the terms:
4 + x = 4.242640687

Solving
4 + x = 4.242640687

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 4.242640687 + -4

Combine like terms: 4 + -4 = 0
0 + x = 4.242640687 + -4
x = 4.242640687 + -4

Combine like terms: 4.242640687 + -4 = 0.242640687
x = 0.242640687

Simplifying
x = 0.242640687


Subproblem 2
x + 4 = -4.242640687

Simplifying
x + 4 = -4.242640687

Reorder the terms:
4 + x = -4.242640687

Solving
4 + x = -4.242640687

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -4.242640687 + -4

Combine like terms: 4 + -4 = 0
0 + x = -4.242640687 + -4
x = -4.242640687 + -4

Combine like terms: -4.242640687 + -4 = -8.242640687
x = -8.242640687

Simplifying
x = -8.242640687


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.242640687, -8.242640687}
Solution
x = {0.242640687, -8.242640687}

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