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Simplifying (9x + -7y)(9x + 5y) = 0 Multiply (9x + -7y) * (9x + 5y) (9x * (9x + 5y) + -7y * (9x + 5y)) = 0 ((9x * 9x + 5y * 9x) + -7y * (9x + 5y)) = 0 Reorder the terms: ((45xy + 81x2) + -7y * (9x + 5y)) = 0 ((45xy + 81x2) + -7y * (9x + 5y)) = 0 (45xy + 81x2 + (9x * -7y + 5y * -7y)) = 0 (45xy + 81x2 + (-63xy + -35y2)) = 0 Reorder the terms: (45xy + -63xy + 81x2 + -35y2) = 0 Combine like terms: 45xy + -63xy = -18xy (-18xy + 81x2 + -35y2) = 0 Solving -18xy + 81x2 + -35y2 = 0 Solving for variable 'x'. Factor a trinomial. (9x + -7y)(9x + 5y) = 0Subproblem 1
Set the factor '(9x + -7y)' equal to zero and attempt to solve: Simplifying 9x + -7y = 0 Solving 9x + -7y = 0 Move all terms containing x to the left, all other terms to the right. Add '7y' to each side of the equation. 9x + -7y + 7y = 0 + 7y Combine like terms: -7y + 7y = 0 9x + 0 = 0 + 7y 9x = 0 + 7y Remove the zero: 9x = 7y Divide each side by '9'. x = 0.7777777778y Simplifying x = 0.7777777778ySubproblem 2
Set the factor '(9x + 5y)' equal to zero and attempt to solve: Simplifying 9x + 5y = 0 Solving 9x + 5y = 0 Move all terms containing x to the left, all other terms to the right. Add '-5y' to each side of the equation. 9x + 5y + -5y = 0 + -5y Combine like terms: 5y + -5y = 0 9x + 0 = 0 + -5y 9x = 0 + -5y Remove the zero: 9x = -5y Divide each side by '9'. x = -0.5555555556y Simplifying x = -0.5555555556ySolution
x = {0.7777777778y, -0.5555555556y}
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