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Simplifying 8x2 + -24xy + -32y2 = 0 Reorder the terms: -24xy + 8x2 + -32y2 = 0 Solving -24xy + 8x2 + -32y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8'. 8(-3xy + x2 + -4y2) = 0 Factor a trinomial. 8((x + -4y)(x + y)) = 0 Ignore the factor 8.Subproblem 1
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 = 4ySubproblem 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 = {4y, -1y}
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