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Simplifying -16a2 + -8a + 1 = 0 Reorder the terms: 1 + -8a + -16a2 = 0 Solving 1 + -8a + -16a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.0625 + 0.5a + a2 = 0 Move the constant term to the right: Add '0.0625' to each side of the equation. -0.0625 + 0.5a + 0.0625 + a2 = 0 + 0.0625 Reorder the terms: -0.0625 + 0.0625 + 0.5a + a2 = 0 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + 0.5a + a2 = 0 + 0.0625 0.5a + a2 = 0 + 0.0625 Combine like terms: 0 + 0.0625 = 0.0625 0.5a + a2 = 0.0625 The a term is 0.5a. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5a + 0.0625 + a2 = 0.0625 + 0.0625 Reorder the terms: 0.0625 + 0.5a + a2 = 0.0625 + 0.0625 Combine like terms: 0.0625 + 0.0625 = 0.125 0.0625 + 0.5a + a2 = 0.125 Factor a perfect square on the left side: (a + 0.25)(a + 0.25) = 0.125 Calculate the square root of the right side: 0.353553391 Break this problem into two subproblems by setting (a + 0.25) equal to 0.353553391 and -0.353553391.Subproblem 1
a + 0.25 = 0.353553391 Simplifying a + 0.25 = 0.353553391 Reorder the terms: 0.25 + a = 0.353553391 Solving 0.25 + a = 0.353553391 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + a = 0.353553391 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + a = 0.353553391 + -0.25 a = 0.353553391 + -0.25 Combine like terms: 0.353553391 + -0.25 = 0.103553391 a = 0.103553391 Simplifying a = 0.103553391Subproblem 2
a + 0.25 = -0.353553391 Simplifying a + 0.25 = -0.353553391 Reorder the terms: 0.25 + a = -0.353553391 Solving 0.25 + a = -0.353553391 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + a = -0.353553391 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + a = -0.353553391 + -0.25 a = -0.353553391 + -0.25 Combine like terms: -0.353553391 + -0.25 = -0.603553391 a = -0.603553391 Simplifying a = -0.603553391Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.103553391, -0.603553391}
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