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Simplifying 18a2 + -240 = -114a Reorder the terms: -240 + 18a2 = -114a Solving -240 + 18a2 = -114a Solving for variable 'a'. Reorder the terms: -240 + 114a + 18a2 = -114a + 114a Combine like terms: -114a + 114a = 0 -240 + 114a + 18a2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-40 + 19a + 3a2) = 0 Factor a trinomial. 6((-8 + -1a)(5 + -3a)) = 0 Ignore the factor 6.Subproblem 1
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 = -8Subproblem 2
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 = 1.666666667Solution
a = {-8, 1.666666667}
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