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Simplifying 15x2 + 31xy + 14y2 = 0 Reorder the terms: 31xy + 15x2 + 14y2 = 0 Solving 31xy + 15x2 + 14y2 = 0 Solving for variable 'x'. Factor a trinomial. (3x + 2y)(5x + 7y) = 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 '(5x + 7y)' equal to zero and attempt to solve: Simplifying 5x + 7y = 0 Solving 5x + 7y = 0 Move all terms containing x to the left, all other terms to the right. Add '-7y' to each side of the equation. 5x + 7y + -7y = 0 + -7y Combine like terms: 7y + -7y = 0 5x + 0 = 0 + -7y 5x = 0 + -7y Remove the zero: 5x = -7y Divide each side by '5'. x = -1.4y Simplifying x = -1.4ySolution
x = {-0.6666666667y, -1.4y}
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