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Simplifying 60x2 + 56xy + -32y2 = 0 Reorder the terms: 56xy + 60x2 + -32y2 = 0 Solving 56xy + 60x2 + -32y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(14xy + 15x2 + -8y2) = 0 Factor a trinomial. 4((5x + -2y)(3x + 4y)) = 0 Ignore the factor 4.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 '(3x + 4y)' equal to zero and attempt to solve: Simplifying 3x + 4y = 0 Solving 3x + 4y = 0 Move all terms containing x to the left, all other terms to the right. Add '-4y' to each side of the equation. 3x + 4y + -4y = 0 + -4y Combine like terms: 4y + -4y = 0 3x + 0 = 0 + -4y 3x = 0 + -4y Remove the zero: 3x = -4y Divide each side by '3'. x = -1.333333333y Simplifying x = -1.333333333ySolution
x = {0.4y, -1.333333333y}
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