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Simplifying -1(5a + 2)(8a + 5) = 0 Reorder the terms: -1(2 + 5a)(8a + 5) = 0 Reorder the terms: -1(2 + 5a)(5 + 8a) = 0 Multiply (2 + 5a) * (5 + 8a) -1(2(5 + 8a) + 5a * (5 + 8a)) = 0 -1((5 * 2 + 8a * 2) + 5a * (5 + 8a)) = 0 -1((10 + 16a) + 5a * (5 + 8a)) = 0 -1(10 + 16a + (5 * 5a + 8a * 5a)) = 0 -1(10 + 16a + (25a + 40a2)) = 0 Combine like terms: 16a + 25a = 41a -1(10 + 41a + 40a2) = 0 (10 * -1 + 41a * -1 + 40a2 * -1) = 0 (-10 + -41a + -40a2) = 0 Solving -10 + -41a + -40a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '-1'. -1(10 + 41a + 40a2) = 0 Factor a trinomial. -1((5 + 8a)(2 + 5a)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 8a)' equal to zero and attempt to solve: Simplifying 5 + 8a = 0 Solving 5 + 8a = 0 Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 8a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 8a = 0 + -5 8a = 0 + -5 Combine like terms: 0 + -5 = -5 8a = -5 Divide each side by '8'. a = -0.625 Simplifying a = -0.625Subproblem 2
Set the factor '(2 + 5a)' equal to zero and attempt to solve: Simplifying 2 + 5a = 0 Solving 2 + 5a = 0 Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 5a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5a = 0 + -2 5a = 0 + -2 Combine like terms: 0 + -2 = -2 5a = -2 Divide each side by '5'. a = -0.4 Simplifying a = -0.4Solution
a = {-0.625, -0.4}
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