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Simplifying (3a + 4)(a + 6) = 17 Reorder the terms: (4 + 3a)(a + 6) = 17 Reorder the terms: (4 + 3a)(6 + a) = 17 Multiply (4 + 3a) * (6 + a) (4(6 + a) + 3a * (6 + a)) = 17 ((6 * 4 + a * 4) + 3a * (6 + a)) = 17 ((24 + 4a) + 3a * (6 + a)) = 17 (24 + 4a + (6 * 3a + a * 3a)) = 17 (24 + 4a + (18a + 3a2)) = 17 Combine like terms: 4a + 18a = 22a (24 + 22a + 3a2) = 17 Solving 24 + 22a + 3a2 = 17 Solving for variable 'a'. Reorder the terms: 24 + -17 + 22a + 3a2 = 17 + -17 Combine like terms: 24 + -17 = 7 7 + 22a + 3a2 = 17 + -17 Combine like terms: 17 + -17 = 0 7 + 22a + 3a2 = 0 Factor a trinomial. (7 + a)(1 + 3a) = 0Subproblem 1
Set the factor '(7 + a)' equal to zero and attempt to solve: Simplifying 7 + a = 0 Solving 7 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + a = 0 + -7 a = 0 + -7 Combine like terms: 0 + -7 = -7 a = -7 Simplifying a = -7Subproblem 2
Set the factor '(1 + 3a)' equal to zero and attempt to solve: Simplifying 1 + 3a = 0 Solving 1 + 3a = 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 + 3a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3a = 0 + -1 3a = 0 + -1 Combine like terms: 0 + -1 = -1 3a = -1 Divide each side by '3'. a = -0.3333333333 Simplifying a = -0.3333333333Solution
a = {-7, -0.3333333333}
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