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Simplifying 0 = 3x2 + 7xy + 2y2 Reorder the terms: 0 = 7xy + 3x2 + 2y2 Solving 0 = 7xy + 3x2 + 2y2 Solving for variable 'x'. Remove the zero: -7xy + -3x2 + -2y2 = 7xy + 3x2 + 2y2 + -7xy + -3x2 + -2y2 Reorder the terms: -7xy + -3x2 + -2y2 = 7xy + -7xy + 3x2 + -3x2 + 2y2 + -2y2 Combine like terms: 7xy + -7xy = 0 -7xy + -3x2 + -2y2 = 0 + 3x2 + -3x2 + 2y2 + -2y2 -7xy + -3x2 + -2y2 = 3x2 + -3x2 + 2y2 + -2y2 Combine like terms: 3x2 + -3x2 = 0 -7xy + -3x2 + -2y2 = 0 + 2y2 + -2y2 -7xy + -3x2 + -2y2 = 2y2 + -2y2 Combine like terms: 2y2 + -2y2 = 0 -7xy + -3x2 + -2y2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(7xy + 3x2 + 2y2) = 0 Factor a trinomial. -1((3x + y)(x + 2y)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3x + y)' equal to zero and attempt to solve: Simplifying 3x + y = 0 Solving 3x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. 3x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 3x + 0 = 0 + -1y 3x = 0 + -1y Remove the zero: 3x = -1y Divide each side by '3'. x = -0.3333333333y Simplifying x = -0.3333333333ySubproblem 2
Set the factor '(x + 2y)' equal to zero and attempt to solve: Simplifying x + 2y = 0 Solving x + 2y = 0 Move all terms containing x to the left, all other terms to the right. Add '-2y' to each side of the equation. x + 2y + -2y = 0 + -2y Combine like terms: 2y + -2y = 0 x + 0 = 0 + -2y x = 0 + -2y Remove the zero: x = -2y Simplifying x = -2ySolution
x = {-0.3333333333y, -2y}
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