y^2-2x^2y=1

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Solution for y^2-2x^2y=1 equation: 


Simplifying
y2 + -2x2y = 1

Reorder the terms:
-2x2y + y2 = 1

Solving
-2x2y + y2 = 1

Solving for variable 'x'.

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

Add '-1y2' to each side of the equation.
-2x2y + y2 + -1y2 = 1 + -1y2

Combine like terms: y2 + -1y2 = 0
-2x2y + 0 = 1 + -1y2
-2x2y = 1 + -1y2

Divide each side by '-2y'.
x2 = -0.5y-1 + 0.5y

Simplifying
x2 = -0.5y-1 + 0.5y

Reorder the terms:
x2 + 0.5y-1 + -0.5y = -0.5y-1 + 0.5y-1 + 0.5y + -0.5y

Combine like terms: -0.5y-1 + 0.5y-1 = 0.0
x2 + 0.5y-1 + -0.5y = 0.0 + 0.5y + -0.5y
x2 + 0.5y-1 + -0.5y = 0.5y + -0.5y

Combine like terms: 0.5y + -0.5y = 0.0
x2 + 0.5y-1 + -0.5y = 0.0

Factor out the Greatest Common Factor (GCF), 'y-1'.
y-1(x2y + 0.5 + -0.5y2) = 0.0


Subproblem 1
Set the factor 'y-1' equal to zero and attempt to solve:

Simplifying
y-1 = 0

Solving
y-1 = 0

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

Add '-1y-1' to each side of the equation.
y-1 + -1y-1 = 0 + -1y-1
Remove the zero:
0 = -1y-1

Simplifying
0 = -1y-1

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 '(x2y + 0.5 + -0.5y2)' equal to zero and attempt to solve:

Simplifying
x2y + 0.5 + -0.5y2 = 0

Reorder the terms:
0.5 + x2y + -0.5y2 = 0

Solving
0.5 + x2y + -0.5y2 = 0

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

Add '-0.5' to each side of the equation.
0.5 + x2y + -0.5 + -0.5y2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + x2y + -0.5y2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x2y + -0.5y2 = 0 + -0.5
x2y + -0.5y2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
x2y + -0.5y2 = -0.5

Add '0.5y2' to each side of the equation.
x2y + -0.5y2 + 0.5y2 = -0.5 + 0.5y2

Combine like terms: -0.5y2 + 0.5y2 = 0.0
x2y + 0.0 = -0.5 + 0.5y2
x2y = -0.5 + 0.5y2

Divide each side by 'y'.
x2 = -0.5y-1 + 0.5y

Simplifying
x2 = -0.5y-1 + 0.5y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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