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Simplifying 24x2 + -3xy + -8xy + y2 = 0 Reorder the terms: -3xy + -8xy + 24x2 + y2 = 0 Combine like terms: -3xy + -8xy = -11xy -11xy + 24x2 + y2 = 0 Solving -11xy + 24x2 + y2 = 0 Solving for variable 'x'. Factor a trinomial. (3x + -1y)(8x + -1y) = 0Subproblem 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 '(8x + -1y)' equal to zero and attempt to solve: Simplifying 8x + -1y = 0 Solving 8x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. 8x + -1y + y = 0 + y Combine like terms: -1y + y = 0 8x + 0 = 0 + y 8x = 0 + y Remove the zero: 8x = y Divide each side by '8'. x = 0.125y Simplifying x = 0.125ySolution
x = {0.3333333333y, 0.125y}
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