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Simplifying 24x2 + -7xy + -6y2 = 0 Reorder the terms: -7xy + 24x2 + -6y2 = 0 Solving -7xy + 24x2 + -6y2 = 0 Solving for variable 'x'. Factor a trinomial. (3x + -2y)(8x + 3y) = 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 '(8x + 3y)' equal to zero and attempt to solve: Simplifying 8x + 3y = 0 Solving 8x + 3y = 0 Move all terms containing x to the left, all other terms to the right. Add '-3y' to each side of the equation. 8x + 3y + -3y = 0 + -3y Combine like terms: 3y + -3y = 0 8x + 0 = 0 + -3y 8x = 0 + -3y Remove the zero: 8x = -3y Divide each side by '8'. x = -0.375y Simplifying x = -0.375ySolution
x = {0.6666666667y, -0.375y}
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