-X^2+2Y^2=1

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Solution for -X^2+2Y^2=1 equation:


Simplifying
-1X2 + 2Y2 = 1

Solving
-1X2 + 2Y2 = 1

Solving for variable 'X'.

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

Add '-2Y2' to each side of the equation.
-1X2 + 2Y2 + -2Y2 = 1 + -2Y2

Combine like terms: 2Y2 + -2Y2 = 0
-1X2 + 0 = 1 + -2Y2
-1X2 = 1 + -2Y2

Divide each side by '-1'.
X2 = -1 + 2Y2

Simplifying
X2 = -1 + 2Y2

Reorder the terms:
1 + X2 + -2Y2 = -1 + 2Y2 + 1 + -2Y2

Reorder the terms:
1 + X2 + -2Y2 = -1 + 1 + 2Y2 + -2Y2

Combine like terms: -1 + 1 = 0
1 + X2 + -2Y2 = 0 + 2Y2 + -2Y2
1 + X2 + -2Y2 = 2Y2 + -2Y2

Combine like terms: 2Y2 + -2Y2 = 0
1 + X2 + -2Y2 = 0

Factor a trinomial.
(X + -1Y)(X + 2Y) = 0

Subproblem 1

Set the factor '(X + -1Y)' equal to zero and attempt to solve: Simplifying X + -1Y = 0 Solving X + -1Y = 0 Move all terms containing X to the left, all other terms to the right. Add 'Y' to each side of the equation. X + -1Y + Y = 0 + Y Combine like terms: -1Y + Y = 0 X + 0 = 0 + Y X = 0 + Y Remove the zero: X = Y Simplifying X = Y

Subproblem 2

Set the factor '(X + 2Y)' equal to zero and attempt to solve: Simplifying X + 2Y = 0 Solving X + 2Y = 0 Move all terms containing X to the left, all other terms to the right. Add '-2Y' to each side of the equation. X + 2Y + -2Y = 0 + -2Y Combine like terms: 2Y + -2Y = 0 X + 0 = 0 + -2Y X = 0 + -2Y Remove the zero: X = -2Y Simplifying X = -2Y

Solution

X = {Y, -2Y}

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