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Simplifying 4a2 + 38a + 34 = 0 Reorder the terms: 34 + 38a + 4a2 = 0 Solving 34 + 38a + 4a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(17 + 19a + 2a2) = 0 Factor a trinomial. 2((17 + 2a)(1 + a)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(17 + 2a)' equal to zero and attempt to solve: Simplifying 17 + 2a = 0 Solving 17 + 2a = 0 Move all terms containing a to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + 2a = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 2a = 0 + -17 2a = 0 + -17 Combine like terms: 0 + -17 = -17 2a = -17 Divide each side by '2'. a = -8.5 Simplifying a = -8.5Subproblem 2
Set the factor '(1 + a)' equal to zero and attempt to solve: Simplifying 1 + a = 0 Solving 1 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + a = 0 + -1 a = 0 + -1 Combine like terms: 0 + -1 = -1 a = -1 Simplifying a = -1Solution
a = {-8.5, -1}
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