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Simplifying (2a + 9)(5a + -1) = 0 Reorder the terms: (9 + 2a)(5a + -1) = 0 Reorder the terms: (9 + 2a)(-1 + 5a) = 0 Multiply (9 + 2a) * (-1 + 5a) (9(-1 + 5a) + 2a * (-1 + 5a)) = 0 ((-1 * 9 + 5a * 9) + 2a * (-1 + 5a)) = 0 ((-9 + 45a) + 2a * (-1 + 5a)) = 0 (-9 + 45a + (-1 * 2a + 5a * 2a)) = 0 (-9 + 45a + (-2a + 10a2)) = 0 Combine like terms: 45a + -2a = 43a (-9 + 43a + 10a2) = 0 Solving -9 + 43a + 10a2 = 0 Solving for variable 'a'. Factor a trinomial. (-9 + -2a)(1 + -5a) = 0Subproblem 1
Set the factor '(-9 + -2a)' equal to zero and attempt to solve: Simplifying -9 + -2a = 0 Solving -9 + -2a = 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 + -2a = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2a = 0 + 9 -2a = 0 + 9 Combine like terms: 0 + 9 = 9 -2a = 9 Divide each side by '-2'. a = -4.5 Simplifying a = -4.5Subproblem 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 = {-4.5, 0.2}
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