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Simplifying 36x2 + -96xy + 64y2 = 0 Reorder the terms: -96xy + 36x2 + 64y2 = 0 Solving -96xy + 36x2 + 64y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-24xy + 9x2 + 16y2) = 0 Factor a trinomial. 4((3x + -4y)(3x + -4y)) = 0 Ignore the factor 4.Subproblem 1
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 = 1.333333333ySubproblem 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 = {1.333333333y, 1.333333333y}
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