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Simplifying 27a2 + -18ab + 3b2 = 0 Reorder the terms: -18ab + 27a2 + 3b2 = 0 Solving -18ab + 27a2 + 3b2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3'. 3(-6ab + 9a2 + b2) = 0 Factor a trinomial. 3((3a + -1b)(3a + -1b)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3a + -1b)' equal to zero and attempt to solve: Simplifying 3a + -1b = 0 Solving 3a + -1b = 0 Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. 3a + -1b + b = 0 + b Combine like terms: -1b + b = 0 3a + 0 = 0 + b 3a = 0 + b Remove the zero: 3a = b Divide each side by '3'. a = 0.3333333333b Simplifying a = 0.3333333333bSubproblem 2
Set the factor '(3a + -1b)' equal to zero and attempt to solve: Simplifying 3a + -1b = 0 Solving 3a + -1b = 0 Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. 3a + -1b + b = 0 + b Combine like terms: -1b + b = 0 3a + 0 = 0 + b 3a = 0 + b Remove the zero: 3a = b Divide each side by '3'. a = 0.3333333333b Simplifying a = 0.3333333333bSolution
a = {0.3333333333b, 0.3333333333b}
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