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Simplifying (a + 8)(a + 3) = 36 Reorder the terms: (8 + a)(a + 3) = 36 Reorder the terms: (8 + a)(3 + a) = 36 Multiply (8 + a) * (3 + a) (8(3 + a) + a(3 + a)) = 36 ((3 * 8 + a * 8) + a(3 + a)) = 36 ((24 + 8a) + a(3 + a)) = 36 (24 + 8a + (3 * a + a * a)) = 36 (24 + 8a + (3a + a2)) = 36 Combine like terms: 8a + 3a = 11a (24 + 11a + a2) = 36 Solving 24 + 11a + a2 = 36 Solving for variable 'a'. Reorder the terms: 24 + -36 + 11a + a2 = 36 + -36 Combine like terms: 24 + -36 = -12 -12 + 11a + a2 = 36 + -36 Combine like terms: 36 + -36 = 0 -12 + 11a + a2 = 0 Factor a trinomial. (-12 + -1a)(1 + -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 '(1 + -1a)' equal to zero and attempt to solve: Simplifying 1 + -1a = 0 Solving 1 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1a = 0 + -1 -1a = 0 + -1 Combine like terms: 0 + -1 = -1 -1a = -1 Divide each side by '-1'. a = 1 Simplifying a = 1Solution
a = {-12, 1}
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