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Simplifying 12x2 + -13xy + -35y2 = 0 Reorder the terms: -13xy + 12x2 + -35y2 = 0 Solving -13xy + 12x2 + -35y2 = 0 Solving for variable 'x'. Factor a trinomial. (3x + -7y)(4x + 5y) = 0Subproblem 1
Set the factor '(3x + -7y)' equal to zero and attempt to solve: Simplifying 3x + -7y = 0 Solving 3x + -7y = 0 Move all terms containing x to the left, all other terms to the right. Add '7y' to each side of the equation. 3x + -7y + 7y = 0 + 7y Combine like terms: -7y + 7y = 0 3x + 0 = 0 + 7y 3x = 0 + 7y Remove the zero: 3x = 7y Divide each side by '3'. x = 2.333333333y Simplifying x = 2.333333333ySubproblem 2
Set the factor '(4x + 5y)' equal to zero and attempt to solve: Simplifying 4x + 5y = 0 Solving 4x + 5y = 0 Move all terms containing x to the left, all other terms to the right. Add '-5y' to each side of the equation. 4x + 5y + -5y = 0 + -5y Combine like terms: 5y + -5y = 0 4x + 0 = 0 + -5y 4x = 0 + -5y Remove the zero: 4x = -5y Divide each side by '4'. x = -1.25y Simplifying x = -1.25ySolution
x = {2.333333333y, -1.25y}
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