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Simplifying -2x2 + 8xy + 64y2 = 0 Reorder the terms: 8xy + -2x2 + 64y2 = 0 Solving 8xy + -2x2 + 64y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(4xy + -1x2 + 32y2) = 0 Factor a trinomial. 2((-1x + -4y)(x + -8y)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1x + -4y)' equal to zero and attempt to solve: Simplifying -1x + -4y = 0 Solving -1x + -4y = 0 Move all terms containing x to the left, all other terms to the right. Add '4y' to each side of the equation. -1x + -4y + 4y = 0 + 4y Combine like terms: -4y + 4y = 0 -1x + 0 = 0 + 4y -1x = 0 + 4y Remove the zero: -1x = 4y Divide each side by '-1'. x = -4y Simplifying x = -4ySubproblem 2
Set the factor '(x + -8y)' equal to zero and attempt to solve: Simplifying x + -8y = 0 Solving x + -8y = 0 Move all terms containing x to the left, all other terms to the right. Add '8y' to each side of the equation. x + -8y + 8y = 0 + 8y Combine like terms: -8y + 8y = 0 x + 0 = 0 + 8y x = 0 + 8y Remove the zero: x = 8y Simplifying x = 8ySolution
x = {-4y, 8y}
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