x^4-4X^2+y^2-6y+6=0

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Solution for x^4-4X^2+y^2-6y+6=0 equation:


Simplifying
x4 + -4X2 + y2 + -6y + 6 = 0

Reorder the terms:
6 + -4X2 + x4 + -6y + y2 = 0

Solving
6 + -4X2 + x4 + -6y + y2 = 0

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 + -4X2 + x4 + -6y + -6 + y2 = 0 + -6

Reorder the terms:
6 + -6 + -4X2 + x4 + -6y + y2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -4X2 + x4 + -6y + y2 = 0 + -6
-4X2 + x4 + -6y + y2 = 0 + -6

Combine like terms: 0 + -6 = -6
-4X2 + x4 + -6y + y2 = -6

Add '-1x4' to each side of the equation.
-4X2 + x4 + -6y + -1x4 + y2 = -6 + -1x4

Reorder the terms:
-4X2 + x4 + -1x4 + -6y + y2 = -6 + -1x4

Combine like terms: x4 + -1x4 = 0
-4X2 + 0 + -6y + y2 = -6 + -1x4
-4X2 + -6y + y2 = -6 + -1x4

Add '6y' to each side of the equation.
-4X2 + -6y + 6y + y2 = -6 + -1x4 + 6y

Combine like terms: -6y + 6y = 0
-4X2 + 0 + y2 = -6 + -1x4 + 6y
-4X2 + y2 = -6 + -1x4 + 6y

Add '-1y2' to each side of the equation.
-4X2 + y2 + -1y2 = -6 + -1x4 + 6y + -1y2

Combine like terms: y2 + -1y2 = 0
-4X2 + 0 = -6 + -1x4 + 6y + -1y2
-4X2 = -6 + -1x4 + 6y + -1y2

Divide each side by '-4'.
X2 = 1.5 + 0.25x4 + -1.5y + 0.25y2

Simplifying
X2 = 1.5 + 0.25x4 + -1.5y + 0.25y2

Reorder the terms:
-1.5 + X2 + -0.25x4 + 1.5y + -0.25y2 = 1.5 + 0.25x4 + -1.5y + 0.25y2 + -1.5 + -0.25x4 + 1.5y + -0.25y2

Reorder the terms:
-1.5 + X2 + -0.25x4 + 1.5y + -0.25y2 = 1.5 + -1.5 + 0.25x4 + -0.25x4 + -1.5y + 1.5y + 0.25y2 + -0.25y2

Combine like terms: 1.5 + -1.5 = 0.0
-1.5 + X2 + -0.25x4 + 1.5y + -0.25y2 = 0.0 + 0.25x4 + -0.25x4 + -1.5y + 1.5y + 0.25y2 + -0.25y2
-1.5 + X2 + -0.25x4 + 1.5y + -0.25y2 = 0.25x4 + -0.25x4 + -1.5y + 1.5y + 0.25y2 + -0.25y2

Combine like terms: 0.25x4 + -0.25x4 = 0.00
-1.5 + X2 + -0.25x4 + 1.5y + -0.25y2 = 0.00 + -1.5y + 1.5y + 0.25y2 + -0.25y2
-1.5 + X2 + -0.25x4 + 1.5y + -0.25y2 = -1.5y + 1.5y + 0.25y2 + -0.25y2

Combine like terms: -1.5y + 1.5y = 0.0
-1.5 + X2 + -0.25x4 + 1.5y + -0.25y2 = 0.0 + 0.25y2 + -0.25y2
-1.5 + X2 + -0.25x4 + 1.5y + -0.25y2 = 0.25y2 + -0.25y2

Combine like terms: 0.25y2 + -0.25y2 = 0.00
-1.5 + X2 + -0.25x4 + 1.5y + -0.25y2 = 0.00

The solution to this equation could not be determined.

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