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Simplifying 30x2 + 20xy + 45xy + 30y2 = 0 Reorder the terms: 20xy + 45xy + 30x2 + 30y2 = 0 Combine like terms: 20xy + 45xy = 65xy 65xy + 30x2 + 30y2 = 0 Solving 65xy + 30x2 + 30y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(13xy + 6x2 + 6y2) = 0 Factor a trinomial. 5((3x + 2y)(2x + 3y)) = 0 Ignore the factor 5.Subproblem 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 + 3y)' equal to zero and attempt to solve: Simplifying 2x + 3y = 0 Solving 2x + 3y = 0 Move all terms containing x to the left, all other terms to the right. Add '-3y' to each side of the equation. 2x + 3y + -3y = 0 + -3y Combine like terms: 3y + -3y = 0 2x + 0 = 0 + -3y 2x = 0 + -3y Remove the zero: 2x = -3y Divide each side by '2'. x = -1.5y Simplifying x = -1.5ySolution
x = {-0.6666666667y, -1.5y}
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