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Simplifying (2a + -1)(8a + -5) = 0 Reorder the terms: (-1 + 2a)(8a + -5) = 0 Reorder the terms: (-1 + 2a)(-5 + 8a) = 0 Multiply (-1 + 2a) * (-5 + 8a) (-1(-5 + 8a) + 2a * (-5 + 8a)) = 0 ((-5 * -1 + 8a * -1) + 2a * (-5 + 8a)) = 0 ((5 + -8a) + 2a * (-5 + 8a)) = 0 (5 + -8a + (-5 * 2a + 8a * 2a)) = 0 (5 + -8a + (-10a + 16a2)) = 0 Combine like terms: -8a + -10a = -18a (5 + -18a + 16a2) = 0 Solving 5 + -18a + 16a2 = 0 Solving for variable 'a'. Factor a trinomial. (1 + -2a)(5 + -8a) = 0Subproblem 1
Set the factor '(1 + -2a)' equal to zero and attempt to solve: Simplifying 1 + -2a = 0 Solving 1 + -2a = 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 + -2a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2a = 0 + -1 -2a = 0 + -1 Combine like terms: 0 + -1 = -1 -2a = -1 Divide each side by '-2'. a = 0.5 Simplifying a = 0.5Subproblem 2
Set the factor '(5 + -8a)' equal to zero and attempt to solve: Simplifying 5 + -8a = 0 Solving 5 + -8a = 0 Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -8a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -8a = 0 + -5 -8a = 0 + -5 Combine like terms: 0 + -5 = -5 -8a = -5 Divide each side by '-8'. a = 0.625 Simplifying a = 0.625Solution
a = {0.5, 0.625}
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