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Simplifying (a + 11)(a + 5) = 2a + 5a + 11a + 55a + 18a + 55 Reorder the terms: (11 + a)(a + 5) = 2a + 5a + 11a + 55a + 18a + 55 Reorder the terms: (11 + a)(5 + a) = 2a + 5a + 11a + 55a + 18a + 55 Multiply (11 + a) * (5 + a) (11(5 + a) + a(5 + a)) = 2a + 5a + 11a + 55a + 18a + 55 ((5 * 11 + a * 11) + a(5 + a)) = 2a + 5a + 11a + 55a + 18a + 55 ((55 + 11a) + a(5 + a)) = 2a + 5a + 11a + 55a + 18a + 55 (55 + 11a + (5 * a + a * a)) = 2a + 5a + 11a + 55a + 18a + 55 (55 + 11a + (5a + a2)) = 2a + 5a + 11a + 55a + 18a + 55 Combine like terms: 11a + 5a = 16a (55 + 16a + a2) = 2a + 5a + 11a + 55a + 18a + 55 Reorder the terms: 55 + 16a + a2 = 55 + 2a + 5a + 11a + 55a + 18a Combine like terms: 2a + 5a = 7a 55 + 16a + a2 = 55 + 7a + 11a + 55a + 18a Combine like terms: 7a + 11a = 18a 55 + 16a + a2 = 55 + 18a + 55a + 18a Combine like terms: 18a + 55a = 73a 55 + 16a + a2 = 55 + 73a + 18a Combine like terms: 73a + 18a = 91a 55 + 16a + a2 = 55 + 91a Add '-55' to each side of the equation. 55 + 16a + -55 + a2 = 55 + -55 + 91a Reorder the terms: 55 + -55 + 16a + a2 = 55 + -55 + 91a Combine like terms: 55 + -55 = 0 0 + 16a + a2 = 55 + -55 + 91a 16a + a2 = 55 + -55 + 91a Combine like terms: 55 + -55 = 0 16a + a2 = 0 + 91a 16a + a2 = 91a Solving 16a + a2 = 91a Solving for variable 'a'. Reorder the terms: 16a + -91a + a2 = 91a + -91a Combine like terms: 16a + -91a = -75a -75a + a2 = 91a + -91a Combine like terms: 91a + -91a = 0 -75a + a2 = 0 Factor out the Greatest Common Factor (GCF), 'a'. a(-75 + a) = 0Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(-75 + a)' equal to zero and attempt to solve: Simplifying -75 + a = 0 Solving -75 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '75' to each side of the equation. -75 + 75 + a = 0 + 75 Combine like terms: -75 + 75 = 0 0 + a = 0 + 75 a = 0 + 75 Combine like terms: 0 + 75 = 75 a = 75 Simplifying a = 75Solution
a = {0, 75}
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