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Simplifying (1 + -5a)(1 + -8a) = 0 Multiply (1 + -5a) * (1 + -8a) (1(1 + -8a) + -5a * (1 + -8a)) = 0 ((1 * 1 + -8a * 1) + -5a * (1 + -8a)) = 0 ((1 + -8a) + -5a * (1 + -8a)) = 0 (1 + -8a + (1 * -5a + -8a * -5a)) = 0 (1 + -8a + (-5a + 40a2)) = 0 Combine like terms: -8a + -5a = -13a (1 + -13a + 40a2) = 0 Solving 1 + -13a + 40a2 = 0 Solving for variable 'a'. Factor a trinomial. (1 + -8a)(1 + -5a) = 0Subproblem 1
Set the factor '(1 + -8a)' equal to zero and attempt to solve: Simplifying 1 + -8a = 0 Solving 1 + -8a = 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 + -8a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -8a = 0 + -1 -8a = 0 + -1 Combine like terms: 0 + -1 = -1 -8a = -1 Divide each side by '-8'. a = 0.125 Simplifying a = 0.125Subproblem 2
Set the factor '(1 + -5a)' equal to zero and attempt to solve: Simplifying 1 + -5a = 0 Solving 1 + -5a = 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 + -5a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5a = 0 + -1 -5a = 0 + -1 Combine like terms: 0 + -1 = -1 -5a = -1 Divide each side by '-5'. a = 0.2 Simplifying a = 0.2Solution
a = {0.125, 0.2}
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