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Simplifying (a + 11)(11a + 1) = 0 Reorder the terms: (11 + a)(11a + 1) = 0 Reorder the terms: (11 + a)(1 + 11a) = 0 Multiply (11 + a) * (1 + 11a) (11(1 + 11a) + a(1 + 11a)) = 0 ((1 * 11 + 11a * 11) + a(1 + 11a)) = 0 ((11 + 121a) + a(1 + 11a)) = 0 (11 + 121a + (1 * a + 11a * a)) = 0 (11 + 121a + (1a + 11a2)) = 0 Combine like terms: 121a + 1a = 122a (11 + 122a + 11a2) = 0 Solving 11 + 122a + 11a2 = 0 Solving for variable 'a'. Factor a trinomial. (11 + a)(1 + 11a) = 0Subproblem 1
Set the factor '(11 + a)' equal to zero and attempt to solve: Simplifying 11 + a = 0 Solving 11 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + a = 0 + -11 Combine like terms: 11 + -11 = 0 0 + a = 0 + -11 a = 0 + -11 Combine like terms: 0 + -11 = -11 a = -11 Simplifying a = -11Subproblem 2
Set the factor '(1 + 11a)' equal to zero and attempt to solve: Simplifying 1 + 11a = 0 Solving 1 + 11a = 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 + 11a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 11a = 0 + -1 11a = 0 + -1 Combine like terms: 0 + -1 = -1 11a = -1 Divide each side by '11'. a = -0.09090909091 Simplifying a = -0.09090909091Solution
a = {-11, -0.09090909091}
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