Y^2=2-y^2

Solution for Y^2=2-y^2 equation:

Simplifying
Y2 = 2 + -1y2

Solving
Y2 = 2 + -1y2

Solving for variable 'Y'.

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

Simplifying
Y2 = 2 + -1y2

Reorder the terms:
-2 + Y2 + y2 = 2 + -1y2 + -2 + y2

Reorder the terms:
-2 + Y2 + y2 = 2 + -2 + -1y2 + y2

Combine like terms: 2 + -2 = 0
-2 + Y2 + y2 = 0 + -1y2 + y2
-2 + Y2 + y2 = -1y2 + y2

Combine like terms: -1y2 + y2 = 0
-2 + Y2 + y2 = 0

Factor a trinomial.
(Y + -1y)(Y + -1y) = 0

Subproblem 1
Set the factor '(Y + -1y)' equal to zero and attempt to solve:

Simplifying
Y + -1y = 0

Solving
Y + -1y = 0

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

Add 'y' to each side of the equation.
Y + -1y + y = 0 + y

Combine like terms: -1y + y = 0
Y + 0 = 0 + y
Y = 0 + y
Remove the zero:
Y = y

Simplifying
Y = y
Subproblem 2
Set the factor '(Y + -1y)' equal to zero and attempt to solve:

Simplifying
Y + -1y = 0

Solving
Y + -1y = 0

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

Add 'y' to each side of the equation.
Y + -1y + y = 0 + y

Combine like terms: -1y + y = 0
Y + 0 = 0 + y
Y = 0 + y
Remove the zero:
Y = y

Simplifying
Y = y
Solution
Y = {y, y}