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Simplifying 5x2 + 30xy + 45y2 = 0 Reorder the terms: 30xy + 5x2 + 45y2 = 0 Solving 30xy + 5x2 + 45y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(6xy + x2 + 9y2) = 0 Factor a trinomial. 5((x + 3y)(x + 3y)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(x + 3y)' equal to zero and attempt to solve: Simplifying x + 3y = 0 Solving x + 3y = 0 Move all terms containing x to the left, all other terms to the right. Add '-3y' to each side of the equation. x + 3y + -3y = 0 + -3y Combine like terms: 3y + -3y = 0 x + 0 = 0 + -3y x = 0 + -3y Remove the zero: x = -3y Simplifying x = -3ySubproblem 2
Set the factor '(x + 3y)' equal to zero and attempt to solve: Simplifying x + 3y = 0 Solving x + 3y = 0 Move all terms containing x to the left, all other terms to the right. Add '-3y' to each side of the equation. x + 3y + -3y = 0 + -3y Combine like terms: 3y + -3y = 0 x + 0 = 0 + -3y x = 0 + -3y Remove the zero: x = -3y Simplifying x = -3ySolution
x = {-3y, -3y}
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