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Simplifying a2 = -35 + -12a Solving a2 = -35 + -12a Solving for variable 'a'. Reorder the terms: 35 + 12a + a2 = -35 + -12a + 35 + 12a Reorder the terms: 35 + 12a + a2 = -35 + 35 + -12a + 12a Combine like terms: -35 + 35 = 0 35 + 12a + a2 = 0 + -12a + 12a 35 + 12a + a2 = -12a + 12a Combine like terms: -12a + 12a = 0 35 + 12a + a2 = 0 Factor a trinomial. (7 + a)(5 + a) = 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 '(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 = {-7, -5}
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