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Simplifying (2 + -4a)(9 + -5a) = 0 Multiply (2 + -4a) * (9 + -5a) (2(9 + -5a) + -4a * (9 + -5a)) = 0 ((9 * 2 + -5a * 2) + -4a * (9 + -5a)) = 0 ((18 + -10a) + -4a * (9 + -5a)) = 0 (18 + -10a + (9 * -4a + -5a * -4a)) = 0 (18 + -10a + (-36a + 20a2)) = 0 Combine like terms: -10a + -36a = -46a (18 + -46a + 20a2) = 0 Solving 18 + -46a + 20a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(9 + -23a + 10a2) = 0 Factor a trinomial. 2((1 + -2a)(9 + -5a)) = 0 Ignore the factor 2.Subproblem 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 '(9 + -5a)' equal to zero and attempt to solve: Simplifying 9 + -5a = 0 Solving 9 + -5a = 0 Move all terms containing a to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -5a = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -5a = 0 + -9 -5a = 0 + -9 Combine like terms: 0 + -9 = -9 -5a = -9 Divide each side by '-5'. a = 1.8 Simplifying a = 1.8Solution
a = {0.5, 1.8}
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