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Simplifying 0 = 16a2 + 8a + 1 Reorder the terms: 0 = 1 + 8a + 16a2 Solving 0 = 1 + 8a + 16a2 Solving for variable 'a'. Combine like terms: 0 + -1 = -1 -1 + -8a + -16a2 = 1 + 8a + 16a2 + -1 + -8a + -16a2 Reorder the terms: -1 + -8a + -16a2 = 1 + -1 + 8a + -8a + 16a2 + -16a2 Combine like terms: 1 + -1 = 0 -1 + -8a + -16a2 = 0 + 8a + -8a + 16a2 + -16a2 -1 + -8a + -16a2 = 8a + -8a + 16a2 + -16a2 Combine like terms: 8a + -8a = 0 -1 + -8a + -16a2 = 0 + 16a2 + -16a2 -1 + -8a + -16a2 = 16a2 + -16a2 Combine like terms: 16a2 + -16a2 = 0 -1 + -8a + -16a2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 8a + 16a2) = 0 Factor a trinomial. -1((1 + 4a)(1 + 4a)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + 4a)' equal to zero and attempt to solve: Simplifying 1 + 4a = 0 Solving 1 + 4a = 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 + 4a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4a = 0 + -1 4a = 0 + -1 Combine like terms: 0 + -1 = -1 4a = -1 Divide each side by '4'. a = -0.25 Simplifying a = -0.25Subproblem 2
Set the factor '(1 + 4a)' equal to zero and attempt to solve: Simplifying 1 + 4a = 0 Solving 1 + 4a = 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 + 4a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4a = 0 + -1 4a = 0 + -1 Combine like terms: 0 + -1 = -1 4a = -1 Divide each side by '4'. a = -0.25 Simplifying a = -0.25Solution
a = {-0.25, -0.25}
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