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Simplifying 8a2 + 16a + -40 = 2 Reorder the terms: -40 + 16a + 8a2 = 2 Solving -40 + 16a + 8a2 = 2 Solving for variable 'a'. Reorder the terms: -40 + -2 + 16a + 8a2 = 2 + -2 Combine like terms: -40 + -2 = -42 -42 + 16a + 8a2 = 2 + -2 Combine like terms: 2 + -2 = 0 -42 + 16a + 8a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-21 + 8a + 4a2) = 0 Factor a trinomial. 2((-7 + -2a)(3 + -2a)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + -2a)' equal to zero and attempt to solve: Simplifying -7 + -2a = 0 Solving -7 + -2a = 0 Move all terms containing a to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -2a = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2a = 0 + 7 -2a = 0 + 7 Combine like terms: 0 + 7 = 7 -2a = 7 Divide each side by '-2'. a = -3.5 Simplifying a = -3.5Subproblem 2
Set the factor '(3 + -2a)' equal to zero and attempt to solve: Simplifying 3 + -2a = 0 Solving 3 + -2a = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2a = 0 + -3 -2a = 0 + -3 Combine like terms: 0 + -3 = -3 -2a = -3 Divide each side by '-2'. a = 1.5 Simplifying a = 1.5Solution
a = {-3.5, 1.5}
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