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Simplifying 3a2 = 48 + 18a Solving 3a2 = 48 + 18a Solving for variable 'a'. Reorder the terms: -48 + -18a + 3a2 = 48 + 18a + -48 + -18a Reorder the terms: -48 + -18a + 3a2 = 48 + -48 + 18a + -18a Combine like terms: 48 + -48 = 0 -48 + -18a + 3a2 = 0 + 18a + -18a -48 + -18a + 3a2 = 18a + -18a Combine like terms: 18a + -18a = 0 -48 + -18a + 3a2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-16 + -6a + a2) = 0 Factor a trinomial. 3((-2 + -1a)(8 + -1a)) = 0 Ignore the factor 3.Subproblem 1
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 = -2Subproblem 2
Set the factor '(8 + -1a)' equal to zero and attempt to solve: Simplifying 8 + -1a = 0 Solving 8 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1a = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1a = 0 + -8 -1a = 0 + -8 Combine like terms: 0 + -8 = -8 -1a = -8 Divide each side by '-1'. a = 8 Simplifying a = 8Solution
a = {-2, 8}
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