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Simplifying (1 + -9a)(1 + -4a) = 0 Multiply (1 + -9a) * (1 + -4a) (1(1 + -4a) + -9a * (1 + -4a)) = 0 ((1 * 1 + -4a * 1) + -9a * (1 + -4a)) = 0 ((1 + -4a) + -9a * (1 + -4a)) = 0 (1 + -4a + (1 * -9a + -4a * -9a)) = 0 (1 + -4a + (-9a + 36a2)) = 0 Combine like terms: -4a + -9a = -13a (1 + -13a + 36a2) = 0 Solving 1 + -13a + 36a2 = 0 Solving for variable 'a'. Factor a trinomial. (1 + -9a)(1 + -4a) = 0Subproblem 1
Set the factor '(1 + -9a)' equal to zero and attempt to solve: Simplifying 1 + -9a = 0 Solving 1 + -9a = 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 + -9a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -9a = 0 + -1 -9a = 0 + -1 Combine like terms: 0 + -1 = -1 -9a = -1 Divide each side by '-9'. a = 0.1111111111 Simplifying a = 0.1111111111Subproblem 2
Set the factor '(1 + -4a)' equal to zero and attempt to solve: Simplifying 1 + -4a = 0 Solving 1 + -4a = 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 + -4a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4a = 0 + -1 -4a = 0 + -1 Combine like terms: 0 + -1 = -1 -4a = -1 Divide each side by '-4'. a = 0.25 Simplifying a = 0.25Solution
a = {0.1111111111, 0.25}
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