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Simplifying 36x2 + 21xy + -36y2 = 0 Reorder the terms: 21xy + 36x2 + -36y2 = 0 Solving 21xy + 36x2 + -36y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(7xy + 12x2 + -12y2) = 0 Factor a trinomial. 3((4x + -3y)(3x + 4y)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4x + -3y)' equal to zero and attempt to solve: Simplifying 4x + -3y = 0 Solving 4x + -3y = 0 Move all terms containing x to the left, all other terms to the right. Add '3y' to each side of the equation. 4x + -3y + 3y = 0 + 3y Combine like terms: -3y + 3y = 0 4x + 0 = 0 + 3y 4x = 0 + 3y Remove the zero: 4x = 3y Divide each side by '4'. x = 0.75y Simplifying x = 0.75ySubproblem 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 = {0.75y, -1.333333333y}
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