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Simplifying -5x2 + -31xy + -6y2 = 0 Reorder the terms: -31xy + -5x2 + -6y2 = 0 Solving -31xy + -5x2 + -6y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(31xy + 5x2 + 6y2) = 0 Factor a trinomial. -1((5x + y)(x + 6y)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5x + y)' equal to zero and attempt to solve: Simplifying 5x + y = 0 Solving 5x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. 5x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 5x + 0 = 0 + -1y 5x = 0 + -1y Remove the zero: 5x = -1y Divide each side by '5'. x = -0.2y Simplifying x = -0.2ySubproblem 2
Set the factor '(x + 6y)' equal to zero and attempt to solve: Simplifying x + 6y = 0 Solving x + 6y = 0 Move all terms containing x to the left, all other terms to the right. Add '-6y' to each side of the equation. x + 6y + -6y = 0 + -6y Combine like terms: 6y + -6y = 0 x + 0 = 0 + -6y x = 0 + -6y Remove the zero: x = -6y Simplifying x = -6ySolution
x = {-0.2y, -6y}
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