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Simplifying 10x2 + 7xy + -45y2 = 0 Reorder the terms: 7xy + 10x2 + -45y2 = 0 Solving 7xy + 10x2 + -45y2 = 0 Solving for variable 'x'. Factor a trinomial. (5x + -9y)(2x + 5y) = 0Subproblem 1
Set the factor '(5x + -9y)' equal to zero and attempt to solve: Simplifying 5x + -9y = 0 Solving 5x + -9y = 0 Move all terms containing x to the left, all other terms to the right. Add '9y' to each side of the equation. 5x + -9y + 9y = 0 + 9y Combine like terms: -9y + 9y = 0 5x + 0 = 0 + 9y 5x = 0 + 9y Remove the zero: 5x = 9y Divide each side by '5'. x = 1.8y Simplifying x = 1.8ySubproblem 2
Set the factor '(2x + 5y)' equal to zero and attempt to solve: Simplifying 2x + 5y = 0 Solving 2x + 5y = 0 Move all terms containing x to the left, all other terms to the right. Add '-5y' to each side of the equation. 2x + 5y + -5y = 0 + -5y Combine like terms: 5y + -5y = 0 2x + 0 = 0 + -5y 2x = 0 + -5y Remove the zero: 2x = -5y Divide each side by '2'. x = -2.5y Simplifying x = -2.5ySolution
x = {1.8y, -2.5y}
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