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Simplifying x2 + 2y + -8y2 = 0 Solving x2 + 2y + -8y2 = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2y' to each side of the equation. x2 + 2y + -2y + -8y2 = 0 + -2y Combine like terms: 2y + -2y = 0 x2 + 0 + -8y2 = 0 + -2y x2 + -8y2 = 0 + -2y Remove the zero: x2 + -8y2 = -2y Add '8y2' to each side of the equation. x2 + -8y2 + 8y2 = -2y + 8y2 Combine like terms: -8y2 + 8y2 = 0 x2 + 0 = -2y + 8y2 x2 = -2y + 8y2 Simplifying x2 = -2y + 8y2 Reorder the terms: x2 + 2y + -8y2 = -2y + 2y + 8y2 + -8y2 Combine like terms: -2y + 2y = 0 x2 + 2y + -8y2 = 0 + 8y2 + -8y2 x2 + 2y + -8y2 = 8y2 + -8y2 Combine like terms: 8y2 + -8y2 = 0 x2 + 2y + -8y2 = 0 Factor a trinomial. (x + -2y)(x + 4y) = 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 + 4y)' equal to zero and attempt to solve: Simplifying x + 4y = 0 Solving x + 4y = 0 Move all terms containing x to the left, all other terms to the right. Add '-4y' to each side of the equation. x + 4y + -4y = 0 + -4y Combine like terms: 4y + -4y = 0 x + 0 = 0 + -4y x = 0 + -4y Remove the zero: x = -4y Simplifying x = -4ySolution
x = {2y, -4y}
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