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Simplifying (a + 8)(a + 3) = -4 Reorder the terms: (8 + a)(a + 3) = -4 Reorder the terms: (8 + a)(3 + a) = -4 Multiply (8 + a) * (3 + a) (8(3 + a) + a(3 + a)) = -4 ((3 * 8 + a * 8) + a(3 + a)) = -4 ((24 + 8a) + a(3 + a)) = -4 (24 + 8a + (3 * a + a * a)) = -4 (24 + 8a + (3a + a2)) = -4 Combine like terms: 8a + 3a = 11a (24 + 11a + a2) = -4 Solving 24 + 11a + a2 = -4 Solving for variable 'a'. Reorder the terms: 24 + 4 + 11a + a2 = -4 + 4 Combine like terms: 24 + 4 = 28 28 + 11a + a2 = -4 + 4 Combine like terms: -4 + 4 = 0 28 + 11a + a2 = 0 Factor a trinomial. (7 + a)(4 + 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 '(4 + a)' equal to zero and attempt to solve: Simplifying 4 + a = 0 Solving 4 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + a = 0 + -4 a = 0 + -4 Combine like terms: 0 + -4 = -4 a = -4 Simplifying a = -4Solution
a = {-7, -4}
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