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Simplifying a2 + 7a + -68 = -8 Reorder the terms: -68 + 7a + a2 = -8 Solving -68 + 7a + a2 = -8 Solving for variable 'a'. Reorder the terms: -68 + 8 + 7a + a2 = -8 + 8 Combine like terms: -68 + 8 = -60 -60 + 7a + a2 = -8 + 8 Combine like terms: -8 + 8 = 0 -60 + 7a + a2 = 0 Factor a trinomial. (-12 + -1a)(5 + -1a) = 0Subproblem 1
Set the factor '(-12 + -1a)' equal to zero and attempt to solve: Simplifying -12 + -1a = 0 Solving -12 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -1a = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1a = 0 + 12 -1a = 0 + 12 Combine like terms: 0 + 12 = 12 -1a = 12 Divide each side by '-1'. a = -12 Simplifying a = -12Subproblem 2
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 = 5Solution
a = {-12, 5}
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