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Simplifying 16y2 + 6yx + -27x2 = 0 Reorder the terms: 6xy + -27x2 + 16y2 = 0 Solving 6xy + -27x2 + 16y2 = 0 Solving for variable 'x'. Factor a trinomial. (-3x + -2y)(9x + -8y) = 0Subproblem 1
Set the factor '(-3x + -2y)' equal to zero and attempt to solve: Simplifying -3x + -2y = 0 Solving -3x + -2y = 0 Move all terms containing x to the left, all other terms to the right. Add '2y' to each side of the equation. -3x + -2y + 2y = 0 + 2y Combine like terms: -2y + 2y = 0 -3x + 0 = 0 + 2y -3x = 0 + 2y Remove the zero: -3x = 2y Divide each side by '-3'. x = -0.6666666667y Simplifying x = -0.6666666667ySubproblem 2
Set the factor '(9x + -8y)' equal to zero and attempt to solve: Simplifying 9x + -8y = 0 Solving 9x + -8y = 0 Move all terms containing x to the left, all other terms to the right. Add '8y' to each side of the equation. 9x + -8y + 8y = 0 + 8y Combine like terms: -8y + 8y = 0 9x + 0 = 0 + 8y 9x = 0 + 8y Remove the zero: 9x = 8y Divide each side by '9'. x = 0.8888888889y Simplifying x = 0.8888888889ySolution
x = {-0.6666666667y, 0.8888888889y}
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