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Simplifying (a + -9)(2a + 1) = 0 Reorder the terms: (-9 + a)(2a + 1) = 0 Reorder the terms: (-9 + a)(1 + 2a) = 0 Multiply (-9 + a) * (1 + 2a) (-9(1 + 2a) + a(1 + 2a)) = 0 ((1 * -9 + 2a * -9) + a(1 + 2a)) = 0 ((-9 + -18a) + a(1 + 2a)) = 0 (-9 + -18a + (1 * a + 2a * a)) = 0 (-9 + -18a + (1a + 2a2)) = 0 Combine like terms: -18a + 1a = -17a (-9 + -17a + 2a2) = 0 Solving -9 + -17a + 2a2 = 0 Solving for variable 'a'. Factor a trinomial. (-1 + -2a)(9 + -1a) = 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 '(9 + -1a)' equal to zero and attempt to solve: Simplifying 9 + -1a = 0 Solving 9 + -1a = 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 + -1a = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1a = 0 + -9 -1a = 0 + -9 Combine like terms: 0 + -9 = -9 -1a = -9 Divide each side by '-1'. a = 9 Simplifying a = 9Solution
a = {-0.5, 9}
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