1+y^4=2x^2

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Solution for 1+y^4=2x^2 equation: 


Simplifying
1 + y4 = 2x2

Solving
1 + y4 = 2x2

Solving for variable 'y'.

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

Add '-1' to each side of the equation.
1 + -1 + y4 = -1 + 2x2

Combine like terms: 1 + -1 = 0
0 + y4 = -1 + 2x2
y4 = -1 + 2x2

Simplifying
y4 = -1 + 2x2

Reorder the terms:
1 + -2x2 + y4 = -1 + 2x2 + 1 + -2x2

Reorder the terms:
1 + -2x2 + y4 = -1 + 1 + 2x2 + -2x2

Combine like terms: -1 + 1 = 0
1 + -2x2 + y4 = 0 + 2x2 + -2x2
1 + -2x2 + y4 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
1 + -2x2 + y4 = 0

Factor a trinomial.
(-2x + -1y2)(x + -1y2) = 0


Subproblem 1
Set the factor '(-2x + -1y2)' equal to zero and attempt to solve:

Simplifying
-2x + -1y2 = 0

Solving
-2x + -1y2 = 0

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

Add '2x' to each side of the equation.
-2x + 2x + -1y2 = 0 + 2x

Combine like terms: -2x + 2x = 0
0 + -1y2 = 0 + 2x
-1y2 = 0 + 2x
Remove the zero:
-1y2 = 2x

Divide each side by '-1'.
y2 = -2x

Simplifying
y2 = -2x

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 '(x + -1y2)' equal to zero and attempt to solve:

Simplifying
x + -1y2 = 0

Solving
x + -1y2 = 0

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

Add '-1x' to each side of the equation.
x + -1x + -1y2 = 0 + -1x

Combine like terms: x + -1x = 0
0 + -1y2 = 0 + -1x
-1y2 = 0 + -1x
Remove the zero:
-1y2 = -1x

Divide each side by '-1'.
y2 = x

Simplifying
y2 = x

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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