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Simplifying -27a2 + 27a + 30 = 0 Reorder the terms: 30 + 27a + -27a2 = 0 Solving 30 + 27a + -27a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3'. 3(10 + 9a + -9a2) = 0 Factor a trinomial. 3((5 + -3a)(2 + 3a)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + -3a)' equal to zero and attempt to solve: Simplifying 5 + -3a = 0 Solving 5 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3a = 0 + -5 -3a = 0 + -5 Combine like terms: 0 + -5 = -5 -3a = -5 Divide each side by '-3'. a = 1.666666667 Simplifying a = 1.666666667Subproblem 2
Set the factor '(2 + 3a)' equal to zero and attempt to solve: Simplifying 2 + 3a = 0 Solving 2 + 3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 3a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3a = 0 + -2 3a = 0 + -2 Combine like terms: 0 + -2 = -2 3a = -2 Divide each side by '3'. a = -0.6666666667 Simplifying a = -0.6666666667Solution
a = {1.666666667, -0.6666666667}
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