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Simplifying (8x + 5y)(-9x + 8y) = 0 Multiply (8x + 5y) * (-9x + 8y) (8x * (-9x + 8y) + 5y * (-9x + 8y)) = 0 ((-9x * 8x + 8y * 8x) + 5y * (-9x + 8y)) = 0 Reorder the terms: ((64xy + -72x2) + 5y * (-9x + 8y)) = 0 ((64xy + -72x2) + 5y * (-9x + 8y)) = 0 (64xy + -72x2 + (-9x * 5y + 8y * 5y)) = 0 (64xy + -72x2 + (-45xy + 40y2)) = 0 Reorder the terms: (64xy + -45xy + -72x2 + 40y2) = 0 Combine like terms: 64xy + -45xy = 19xy (19xy + -72x2 + 40y2) = 0 Solving 19xy + -72x2 + 40y2 = 0 Solving for variable 'x'. Factor a trinomial. (-8x + -5y)(9x + -8y) = 0Subproblem 1
Set the factor '(-8x + -5y)' equal to zero and attempt to solve: Simplifying -8x + -5y = 0 Solving -8x + -5y = 0 Move all terms containing x to the left, all other terms to the right. Add '5y' to each side of the equation. -8x + -5y + 5y = 0 + 5y Combine like terms: -5y + 5y = 0 -8x + 0 = 0 + 5y -8x = 0 + 5y Remove the zero: -8x = 5y Divide each side by '-8'. x = -0.625y Simplifying x = -0.625ySubproblem 2
Set the factor '(9x + -8y)' equal to zero and attempt to solve: Simplifying 9x + -8y = 0 Solving 9x + -8y = 0 Move all terms containing x to the left, all other terms to the right. Add '8y' to each side of the equation. 9x + -8y + 8y = 0 + 8y Combine like terms: -8y + 8y = 0 9x + 0 = 0 + 8y 9x = 0 + 8y Remove the zero: 9x = 8y Divide each side by '9'. x = 0.8888888889y Simplifying x = 0.8888888889ySolution
x = {-0.625y, 0.8888888889y}
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