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Simplifying 4(a + 2)(a + 2) + 20(a + 2) + -24 = 0 Reorder the terms: 4(2 + a)(a + 2) + 20(a + 2) + -24 = 0 Reorder the terms: 4(2 + a)(2 + a) + 20(a + 2) + -24 = 0 Multiply (2 + a) * (2 + a) 4(2(2 + a) + a(2 + a)) + 20(a + 2) + -24 = 0 4((2 * 2 + a * 2) + a(2 + a)) + 20(a + 2) + -24 = 0 4((4 + 2a) + a(2 + a)) + 20(a + 2) + -24 = 0 4(4 + 2a + (2 * a + a * a)) + 20(a + 2) + -24 = 0 4(4 + 2a + (2a + a2)) + 20(a + 2) + -24 = 0 Combine like terms: 2a + 2a = 4a 4(4 + 4a + a2) + 20(a + 2) + -24 = 0 (4 * 4 + 4a * 4 + a2 * 4) + 20(a + 2) + -24 = 0 (16 + 16a + 4a2) + 20(a + 2) + -24 = 0 Reorder the terms: 16 + 16a + 4a2 + 20(2 + a) + -24 = 0 16 + 16a + 4a2 + (2 * 20 + a * 20) + -24 = 0 16 + 16a + 4a2 + (40 + 20a) + -24 = 0 Reorder the terms: 16 + 40 + -24 + 16a + 20a + 4a2 = 0 Combine like terms: 16 + 40 = 56 56 + -24 + 16a + 20a + 4a2 = 0 Combine like terms: 56 + -24 = 32 32 + 16a + 20a + 4a2 = 0 Combine like terms: 16a + 20a = 36a 32 + 36a + 4a2 = 0 Solving 32 + 36a + 4a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4'. 4(8 + 9a + a2) = 0 Factor a trinomial. 4((8 + a)(1 + a)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(8 + a)' equal to zero and attempt to solve: Simplifying 8 + a = 0 Solving 8 + a = 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 + a = 0 + -8 Combine like terms: 8 + -8 = 0 0 + a = 0 + -8 a = 0 + -8 Combine like terms: 0 + -8 = -8 a = -8 Simplifying a = -8Subproblem 2
Set the factor '(1 + a)' equal to zero and attempt to solve: Simplifying 1 + a = 0 Solving 1 + a = 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 + a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + a = 0 + -1 a = 0 + -1 Combine like terms: 0 + -1 = -1 a = -1 Simplifying a = -1Solution
a = {-8, -1}
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