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Simplifying 30x2 + 33xy + -18y2 = 0 Reorder the terms: 33xy + 30x2 + -18y2 = 0 Solving 33xy + 30x2 + -18y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(11xy + 10x2 + -6y2) = 0 Factor a trinomial. 3((5x + -2y)(2x + 3y)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5x + -2y)' equal to zero and attempt to solve: Simplifying 5x + -2y = 0 Solving 5x + -2y = 0 Move all terms containing x to the left, all other terms to the right. Add '2y' to each side of the equation. 5x + -2y + 2y = 0 + 2y Combine like terms: -2y + 2y = 0 5x + 0 = 0 + 2y 5x = 0 + 2y Remove the zero: 5x = 2y Divide each side by '5'. x = 0.4y Simplifying x = 0.4ySubproblem 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 = {0.4y, -1.5y}
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