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Simplifying 0 = 9a2 + 24a + 16 Reorder the terms: 0 = 16 + 24a + 9a2 Solving 0 = 16 + 24a + 9a2 Solving for variable 'a'. Combine like terms: 0 + -16 = -16 -16 + -24a + -9a2 = 16 + 24a + 9a2 + -16 + -24a + -9a2 Reorder the terms: -16 + -24a + -9a2 = 16 + -16 + 24a + -24a + 9a2 + -9a2 Combine like terms: 16 + -16 = 0 -16 + -24a + -9a2 = 0 + 24a + -24a + 9a2 + -9a2 -16 + -24a + -9a2 = 24a + -24a + 9a2 + -9a2 Combine like terms: 24a + -24a = 0 -16 + -24a + -9a2 = 0 + 9a2 + -9a2 -16 + -24a + -9a2 = 9a2 + -9a2 Combine like terms: 9a2 + -9a2 = 0 -16 + -24a + -9a2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(16 + 24a + 9a2) = 0 Factor a trinomial. -1((4 + 3a)(4 + 3a)) = 0 Ignore the factor -1.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 '(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 = -1.333333333Solution
a = {-1.333333333, -1.333333333}
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