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Simplifying 8a2 = 18 + 18a Solving 8a2 = 18 + 18a Solving for variable 'a'. Reorder the terms: -18 + -18a + 8a2 = 18 + 18a + -18 + -18a Reorder the terms: -18 + -18a + 8a2 = 18 + -18 + 18a + -18a Combine like terms: 18 + -18 = 0 -18 + -18a + 8a2 = 0 + 18a + -18a -18 + -18a + 8a2 = 18a + -18a Combine like terms: 18a + -18a = 0 -18 + -18a + 8a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + -9a + 4a2) = 0 Factor a trinomial. 2((-3 + -4a)(3 + -1a)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -4a)' equal to zero and attempt to solve: Simplifying -3 + -4a = 0 Solving -3 + -4a = 0 Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -4a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4a = 0 + 3 -4a = 0 + 3 Combine like terms: 0 + 3 = 3 -4a = 3 Divide each side by '-4'. a = -0.75 Simplifying a = -0.75Subproblem 2
Set the factor '(3 + -1a)' equal to zero and attempt to solve: Simplifying 3 + -1a = 0 Solving 3 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1a = 0 + -3 -1a = 0 + -3 Combine like terms: 0 + -3 = -3 -1a = -3 Divide each side by '-1'. a = 3 Simplifying a = 3Solution
a = {-0.75, 3}
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