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Simplifying (4a + 1)(4a + 1) = 0 Reorder the terms: (1 + 4a)(4a + 1) = 0 Reorder the terms: (1 + 4a)(1 + 4a) = 0 Multiply (1 + 4a) * (1 + 4a) (1(1 + 4a) + 4a * (1 + 4a)) = 0 ((1 * 1 + 4a * 1) + 4a * (1 + 4a)) = 0 ((1 + 4a) + 4a * (1 + 4a)) = 0 (1 + 4a + (1 * 4a + 4a * 4a)) = 0 (1 + 4a + (4a + 16a2)) = 0 Combine like terms: 4a + 4a = 8a (1 + 8a + 16a2) = 0 Solving 1 + 8a + 16a2 = 0 Solving for variable 'a'. Factor a trinomial. (1 + 4a)(1 + 4a) = 0Subproblem 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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