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Simplifying x2 + -3y2 = 2 Solving x2 + -3y2 = 2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3y2' to each side of the equation. x2 + -3y2 + 3y2 = 2 + 3y2 Combine like terms: -3y2 + 3y2 = 0 x2 + 0 = 2 + 3y2 x2 = 2 + 3y2 Simplifying x2 = 2 + 3y2 Reorder the terms: -2 + x2 + -3y2 = 2 + 3y2 + -2 + -3y2 Reorder the terms: -2 + x2 + -3y2 = 2 + -2 + 3y2 + -3y2 Combine like terms: 2 + -2 = 0 -2 + x2 + -3y2 = 0 + 3y2 + -3y2 -2 + x2 + -3y2 = 3y2 + -3y2 Combine like terms: 3y2 + -3y2 = 0 -2 + x2 + -3y2 = 0 Factor a trinomial. (x + -3y)(x + y) = 0Subproblem 1
Set the factor '(x + -3y)' equal to zero and attempt to solve: Simplifying x + -3y = 0 Solving x + -3y = 0 Move all terms containing x to the left, all other terms to the right. Add '3y' to each side of the equation. x + -3y + 3y = 0 + 3y Combine like terms: -3y + 3y = 0 x + 0 = 0 + 3y x = 0 + 3y Remove the zero: x = 3y Simplifying x = 3ySubproblem 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 = {3y, -1y}
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