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Simplifying (2a + -1)(a + 8) = 0 Reorder the terms: (-1 + 2a)(a + 8) = 0 Reorder the terms: (-1 + 2a)(8 + a) = 0 Multiply (-1 + 2a) * (8 + a) (-1(8 + a) + 2a * (8 + a)) = 0 ((8 * -1 + a * -1) + 2a * (8 + a)) = 0 ((-8 + -1a) + 2a * (8 + a)) = 0 (-8 + -1a + (8 * 2a + a * 2a)) = 0 (-8 + -1a + (16a + 2a2)) = 0 Combine like terms: -1a + 16a = 15a (-8 + 15a + 2a2) = 0 Solving -8 + 15a + 2a2 = 0 Solving for variable 'a'. Factor a trinomial. (-8 + -1a)(1 + -2a) = 0Subproblem 1
Set the factor '(-8 + -1a)' equal to zero and attempt to solve: Simplifying -8 + -1a = 0 Solving -8 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1a = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1a = 0 + 8 -1a = 0 + 8 Combine like terms: 0 + 8 = 8 -1a = 8 Divide each side by '-1'. a = -8 Simplifying a = -8Subproblem 2
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 = 0.5Solution
a = {-8, 0.5}
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