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Simplifying 0 = y2 + 6xy + 9x2 Reorder the terms: 0 = 6xy + 9x2 + y2 Solving 0 = 6xy + 9x2 + y2 Solving for variable 'x'. Remove the zero: -6xy + -9x2 + -1y2 = 6xy + 9x2 + y2 + -6xy + -9x2 + -1y2 Reorder the terms: -6xy + -9x2 + -1y2 = 6xy + -6xy + 9x2 + -9x2 + y2 + -1y2 Combine like terms: 6xy + -6xy = 0 -6xy + -9x2 + -1y2 = 0 + 9x2 + -9x2 + y2 + -1y2 -6xy + -9x2 + -1y2 = 9x2 + -9x2 + y2 + -1y2 Combine like terms: 9x2 + -9x2 = 0 -6xy + -9x2 + -1y2 = 0 + y2 + -1y2 -6xy + -9x2 + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -6xy + -9x2 + -1y2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(6xy + 9x2 + y2) = 0 Factor a trinomial. -1((3x + y)(3x + y)) = 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 '(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 = -0.3333333333ySolution
x = {-0.3333333333y, -0.3333333333y}
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