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Simplifying 8b2 + -16b + 1 = 0 Reorder the terms: 1 + -16b + 8b2 = 0 Solving 1 + -16b + 8b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.125 + -2b + b2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + -2b + -0.125 + b2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + -2b + b2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + -2b + b2 = 0 + -0.125 -2b + b2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 -2b + b2 = -0.125 The b term is -2b. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2b + 1 + b2 = -0.125 + 1 Reorder the terms: 1 + -2b + b2 = -0.125 + 1 Combine like terms: -0.125 + 1 = 0.875 1 + -2b + b2 = 0.875 Factor a perfect square on the left side: (b + -1)(b + -1) = 0.875 Calculate the square root of the right side: 0.935414347 Break this problem into two subproblems by setting (b + -1) equal to 0.935414347 and -0.935414347.Subproblem 1
b + -1 = 0.935414347 Simplifying b + -1 = 0.935414347 Reorder the terms: -1 + b = 0.935414347 Solving -1 + b = 0.935414347 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + b = 0.935414347 + 1 Combine like terms: -1 + 1 = 0 0 + b = 0.935414347 + 1 b = 0.935414347 + 1 Combine like terms: 0.935414347 + 1 = 1.935414347 b = 1.935414347 Simplifying b = 1.935414347Subproblem 2
b + -1 = -0.935414347 Simplifying b + -1 = -0.935414347 Reorder the terms: -1 + b = -0.935414347 Solving -1 + b = -0.935414347 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + b = -0.935414347 + 1 Combine like terms: -1 + 1 = 0 0 + b = -0.935414347 + 1 b = -0.935414347 + 1 Combine like terms: -0.935414347 + 1 = 0.064585653 b = 0.064585653 Simplifying b = 0.064585653Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.935414347, 0.064585653}
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