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Simplifying x2 + -2y2 = 1 Solving x2 + -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. x2 + -2y2 + 2y2 = 1 + 2y2 Combine like terms: -2y2 + 2y2 = 0 x2 + 0 = 1 + 2y2 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 + -2y)(x + y) = 0Subproblem 1
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 = 2ySubproblem 2
Set the factor '(x + y)' equal to zero and attempt to solve: Simplifying x + y = 0 Solving x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 x + 0 = 0 + -1y x = 0 + -1y Remove the zero: x = -1y Simplifying x = -1ySolution
x = {2y, -1y}
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