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Simplifying x2 + -6y2 = 1 Solving x2 + -6y2 = 1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6y2' to each side of the equation. x2 + -6y2 + 6y2 = 1 + 6y2 Combine like terms: -6y2 + 6y2 = 0 x2 + 0 = 1 + 6y2 x2 = 1 + 6y2 Simplifying x2 = 1 + 6y2 Reorder the terms: -1 + x2 + -6y2 = 1 + 6y2 + -1 + -6y2 Reorder the terms: -1 + x2 + -6y2 = 1 + -1 + 6y2 + -6y2 Combine like terms: 1 + -1 = 0 -1 + x2 + -6y2 = 0 + 6y2 + -6y2 -1 + x2 + -6y2 = 6y2 + -6y2 Combine like terms: 6y2 + -6y2 = 0 -1 + x2 + -6y2 = 0 Factor a trinomial. (x + -3y)(x + 2y) = 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 + 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 = -2ySolution
x = {3y, -2y}
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