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Simplifying 45x2 + -30xy + 5y2 = 0 Reorder the terms: -30xy + 45x2 + 5y2 = 0 Solving -30xy + 45x2 + 5y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-6xy + 9x2 + y2) = 0 Factor a trinomial. 5((3x + -1y)(3x + -1y)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(3x + -1y)' equal to zero and attempt to solve: Simplifying 3x + -1y = 0 Solving 3x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. 3x + -1y + y = 0 + y Combine like terms: -1y + y = 0 3x + 0 = 0 + y 3x = 0 + y Remove the zero: 3x = y Divide each side by '3'. x = 0.3333333333y Simplifying x = 0.3333333333ySubproblem 2
Set the factor '(3x + -1y)' equal to zero and attempt to solve: Simplifying 3x + -1y = 0 Solving 3x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. 3x + -1y + y = 0 + y Combine like terms: -1y + y = 0 3x + 0 = 0 + y 3x = 0 + y Remove the zero: 3x = y Divide each side by '3'. x = 0.3333333333y Simplifying x = 0.3333333333ySolution
x = {0.3333333333y, 0.3333333333y}
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