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Simplifying 18a2 + -9ab + -27b2 = 0 Reorder the terms: -9ab + 18a2 + -27b2 = 0 Solving -9ab + 18a2 + -27b2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '9'. 9(-1ab + 2a2 + -3b2) = 0 Factor a trinomial. 9((2a + -3b)(a + b)) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(2a + -3b)' equal to zero and attempt to solve: Simplifying 2a + -3b = 0 Solving 2a + -3b = 0 Move all terms containing a to the left, all other terms to the right. Add '3b' to each side of the equation. 2a + -3b + 3b = 0 + 3b Combine like terms: -3b + 3b = 0 2a + 0 = 0 + 3b 2a = 0 + 3b Remove the zero: 2a = 3b Divide each side by '2'. a = 1.5b Simplifying a = 1.5bSubproblem 2
Set the factor '(a + b)' equal to zero and attempt to solve: Simplifying a + b = 0 Solving a + b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. a + b + -1b = 0 + -1b Combine like terms: b + -1b = 0 a + 0 = 0 + -1b a = 0 + -1b Remove the zero: a = -1b Simplifying a = -1bSolution
a = {1.5b, -1b}
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