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Simplifying a2 = -40 + -13a Solving a2 = -40 + -13a Solving for variable 'a'. Reorder the terms: 40 + 13a + a2 = -40 + -13a + 40 + 13a Reorder the terms: 40 + 13a + a2 = -40 + 40 + -13a + 13a Combine like terms: -40 + 40 = 0 40 + 13a + a2 = 0 + -13a + 13a 40 + 13a + a2 = -13a + 13a Combine like terms: -13a + 13a = 0 40 + 13a + a2 = 0 Factor a trinomial. (8 + a)(5 + a) = 0Subproblem 1
Set the factor '(8 + a)' equal to zero and attempt to solve: Simplifying 8 + a = 0 Solving 8 + a = 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 + a = 0 + -8 Combine like terms: 8 + -8 = 0 0 + a = 0 + -8 a = 0 + -8 Combine like terms: 0 + -8 = -8 a = -8 Simplifying a = -8Subproblem 2
Set the factor '(5 + a)' equal to zero and attempt to solve: Simplifying 5 + a = 0 Solving 5 + a = 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 + a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + a = 0 + -5 a = 0 + -5 Combine like terms: 0 + -5 = -5 a = -5 Simplifying a = -5Solution
a = {-8, -5}
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