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Simplifying (7 + 3a)(a * 2 + 5) = 117 Reorder the terms for easier multiplication: (7 + 3a)(2a + 5) = 117 Reorder the terms: (7 + 3a)(5 + 2a) = 117 Multiply (7 + 3a) * (5 + 2a) (7(5 + 2a) + 3a * (5 + 2a)) = 117 ((5 * 7 + 2a * 7) + 3a * (5 + 2a)) = 117 ((35 + 14a) + 3a * (5 + 2a)) = 117 (35 + 14a + (5 * 3a + 2a * 3a)) = 117 (35 + 14a + (15a + 6a2)) = 117 Combine like terms: 14a + 15a = 29a (35 + 29a + 6a2) = 117 Solving 35 + 29a + 6a2 = 117 Solving for variable 'a'. Reorder the terms: 35 + -117 + 29a + 6a2 = 117 + -117 Combine like terms: 35 + -117 = -82 -82 + 29a + 6a2 = 117 + -117 Combine like terms: 117 + -117 = 0 -82 + 29a + 6a2 = 0 Factor a trinomial. (-41 + -6a)(2 + -1a) = 0Subproblem 1
Set the factor '(-41 + -6a)' equal to zero and attempt to solve: Simplifying -41 + -6a = 0 Solving -41 + -6a = 0 Move all terms containing a to the left, all other terms to the right. Add '41' to each side of the equation. -41 + 41 + -6a = 0 + 41 Combine like terms: -41 + 41 = 0 0 + -6a = 0 + 41 -6a = 0 + 41 Combine like terms: 0 + 41 = 41 -6a = 41 Divide each side by '-6'. a = -6.833333333 Simplifying a = -6.833333333Subproblem 2
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 = 2Solution
a = {-6.833333333, 2}
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