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Simplifying -8b * -8b + 2b + -6 = 3 Reorder the terms for easier multiplication: -8 * -8b * b + 2b + -6 = 3 Multiply -8 * -8 64b * b + 2b + -6 = 3 Multiply b * b 64b2 + 2b + -6 = 3 Reorder the terms: -6 + 2b + 64b2 = 3 Solving -6 + 2b + 64b2 = 3 Solving for variable 'b'. Reorder the terms: -6 + -3 + 2b + 64b2 = 3 + -3 Combine like terms: -6 + -3 = -9 -9 + 2b + 64b2 = 3 + -3 Combine like terms: 3 + -3 = 0 -9 + 2b + 64b2 = 0 Begin completing the square. Divide all terms by 64 the coefficient of the squared term: Divide each side by '64'. -0.140625 + 0.03125b + b2 = 0 Move the constant term to the right: Add '0.140625' to each side of the equation. -0.140625 + 0.03125b + 0.140625 + b2 = 0 + 0.140625 Reorder the terms: -0.140625 + 0.140625 + 0.03125b + b2 = 0 + 0.140625 Combine like terms: -0.140625 + 0.140625 = 0.000000 0.000000 + 0.03125b + b2 = 0 + 0.140625 0.03125b + b2 = 0 + 0.140625 Combine like terms: 0 + 0.140625 = 0.140625 0.03125b + b2 = 0.140625 The b term is 0.03125b. Take half its coefficient (0.015625). Square it (0.000244140625) and add it to both sides. Add '0.000244140625' to each side of the equation. 0.03125b + 0.000244140625 + b2 = 0.140625 + 0.000244140625 Reorder the terms: 0.000244140625 + 0.03125b + b2 = 0.140625 + 0.000244140625 Combine like terms: 0.140625 + 0.000244140625 = 0.140869140625 0.000244140625 + 0.03125b + b2 = 0.140869140625 Factor a perfect square on the left side: (b + 0.015625)(b + 0.015625) = 0.140869140625 Calculate the square root of the right side: 0.37532538 Break this problem into two subproblems by setting (b + 0.015625) equal to 0.37532538 and -0.37532538.Subproblem 1
b + 0.015625 = 0.37532538 Simplifying b + 0.015625 = 0.37532538 Reorder the terms: 0.015625 + b = 0.37532538 Solving 0.015625 + b = 0.37532538 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.015625' to each side of the equation. 0.015625 + -0.015625 + b = 0.37532538 + -0.015625 Combine like terms: 0.015625 + -0.015625 = 0.000000 0.000000 + b = 0.37532538 + -0.015625 b = 0.37532538 + -0.015625 Combine like terms: 0.37532538 + -0.015625 = 0.35970038 b = 0.35970038 Simplifying b = 0.35970038Subproblem 2
b + 0.015625 = -0.37532538 Simplifying b + 0.015625 = -0.37532538 Reorder the terms: 0.015625 + b = -0.37532538 Solving 0.015625 + b = -0.37532538 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.015625' to each side of the equation. 0.015625 + -0.015625 + b = -0.37532538 + -0.015625 Combine like terms: 0.015625 + -0.015625 = 0.000000 0.000000 + b = -0.37532538 + -0.015625 b = -0.37532538 + -0.015625 Combine like terms: -0.37532538 + -0.015625 = -0.39095038 b = -0.39095038 Simplifying b = -0.39095038Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.35970038, -0.39095038}
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