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Simplifying 9a2 = 6a + 24 Reorder the terms: 9a2 = 24 + 6a Solving 9a2 = 24 + 6a Solving for variable 'a'. Reorder the terms: -24 + -6a + 9a2 = 24 + 6a + -24 + -6a Reorder the terms: -24 + -6a + 9a2 = 24 + -24 + 6a + -6a Combine like terms: 24 + -24 = 0 -24 + -6a + 9a2 = 0 + 6a + -6a -24 + -6a + 9a2 = 6a + -6a Combine like terms: 6a + -6a = 0 -24 + -6a + 9a2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-8 + -2a + 3a2) = 0 Factor a trinomial. 3((-4 + -3a)(2 + -1a)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + -3a)' equal to zero and attempt to solve: Simplifying -4 + -3a = 0 Solving -4 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -3a = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3a = 0 + 4 -3a = 0 + 4 Combine like terms: 0 + 4 = 4 -3a = 4 Divide each side by '-3'. a = -1.333333333 Simplifying a = -1.333333333Subproblem 2
Set the factor '(2 + -1a)' equal to zero and attempt to solve: Simplifying 2 + -1a = 0 Solving 2 + -1a = 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 + -1a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1a = 0 + -2 -1a = 0 + -2 Combine like terms: 0 + -2 = -2 -1a = -2 Divide each side by '-1'. a = 2 Simplifying a = 2Solution
a = {-1.333333333, 2}
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