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Simplifying 6x2 + 11xy + -10y2 = 0 Reorder the terms: 11xy + 6x2 + -10y2 = 0 Solving 11xy + 6x2 + -10y2 = 0 Solving for variable 'x'. Factor a trinomial. (3x + -2y)(2x + 5y) = 0Subproblem 1
Set the factor '(3x + -2y)' equal to zero and attempt to solve: Simplifying 3x + -2y = 0 Solving 3x + -2y = 0 Move all terms containing x to the left, all other terms to the right. Add '2y' to each side of the equation. 3x + -2y + 2y = 0 + 2y Combine like terms: -2y + 2y = 0 3x + 0 = 0 + 2y 3x = 0 + 2y Remove the zero: 3x = 2y Divide each side by '3'. x = 0.6666666667y Simplifying x = 0.6666666667ySubproblem 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 = {0.6666666667y, -2.5y}
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