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Simplifying 10x2 + 5xy + -30y2 = 0 Reorder the terms: 5xy + 10x2 + -30y2 = 0 Solving 5xy + 10x2 + -30y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(xy + 2x2 + -6y2) = 0 Factor a trinomial. 5((2x + -3y)(x + 2y)) = 0 Ignore the factor 5.Subproblem 1
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 = 1.5ySubproblem 2
Set the factor '(x + 2y)' equal to zero and attempt to solve: Simplifying x + 2y = 0 Solving x + 2y = 0 Move all terms containing x to the left, all other terms to the right. Add '-2y' to each side of the equation. x + 2y + -2y = 0 + -2y Combine like terms: 2y + -2y = 0 x + 0 = 0 + -2y x = 0 + -2y Remove the zero: x = -2y Simplifying x = -2ySolution
x = {1.5y, -2y}
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