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Simplifying 0 = (8x + -5y)(8x + 9y) Multiply (8x + -5y) * (8x + 9y) 0 = (8x * (8x + 9y) + -5y * (8x + 9y)) 0 = ((8x * 8x + 9y * 8x) + -5y * (8x + 9y)) Reorder the terms: 0 = ((72xy + 64x2) + -5y * (8x + 9y)) 0 = ((72xy + 64x2) + -5y * (8x + 9y)) 0 = (72xy + 64x2 + (8x * -5y + 9y * -5y)) 0 = (72xy + 64x2 + (-40xy + -45y2)) Reorder the terms: 0 = (72xy + -40xy + 64x2 + -45y2) Combine like terms: 72xy + -40xy = 32xy 0 = (32xy + 64x2 + -45y2) Solving 0 = 32xy + 64x2 + -45y2 Solving for variable 'x'. Remove the zero: -32xy + -64x2 + 45y2 = 32xy + 64x2 + -45y2 + -32xy + -64x2 + 45y2 Reorder the terms: -32xy + -64x2 + 45y2 = 32xy + -32xy + 64x2 + -64x2 + -45y2 + 45y2 Combine like terms: 32xy + -32xy = 0 -32xy + -64x2 + 45y2 = 0 + 64x2 + -64x2 + -45y2 + 45y2 -32xy + -64x2 + 45y2 = 64x2 + -64x2 + -45y2 + 45y2 Combine like terms: 64x2 + -64x2 = 0 -32xy + -64x2 + 45y2 = 0 + -45y2 + 45y2 -32xy + -64x2 + 45y2 = -45y2 + 45y2 Combine like terms: -45y2 + 45y2 = 0 -32xy + -64x2 + 45y2 = 0 Factor a trinomial. (-8x + -9y)(8x + -5y) = 0Subproblem 1
Set the factor '(-8x + -9y)' equal to zero and attempt to solve: Simplifying -8x + -9y = 0 Solving -8x + -9y = 0 Move all terms containing x to the left, all other terms to the right. Add '9y' to each side of the equation. -8x + -9y + 9y = 0 + 9y Combine like terms: -9y + 9y = 0 -8x + 0 = 0 + 9y -8x = 0 + 9y Remove the zero: -8x = 9y Divide each side by '-8'. x = -1.125y Simplifying x = -1.125ySubproblem 2
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 = 0.625ySolution
x = {-1.125y, 0.625y}
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