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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. (5 + -1a)(8 + -1a) = 0Subproblem 1
Set the factor '(5 + -1a)' equal to zero and attempt to solve: Simplifying 5 + -1a = 0 Solving 5 + -1a = 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 + -1a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1a = 0 + -5 -1a = 0 + -5 Combine like terms: 0 + -5 = -5 -1a = -5 Divide each side by '-1'. a = 5 Simplifying a = 5Subproblem 2
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 = 8Solution
a = {5, 8}
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