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Simplifying 56b2 + b + 1 = 0 Reorder the terms: 1 + b + 56b2 = 0 Solving 1 + b + 56b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 56 the coefficient of the squared term: Divide each side by '56'. 0.01785714286 + 0.01785714286b + b2 = 0 Move the constant term to the right: Add '-0.01785714286' to each side of the equation. 0.01785714286 + 0.01785714286b + -0.01785714286 + b2 = 0 + -0.01785714286 Reorder the terms: 0.01785714286 + -0.01785714286 + 0.01785714286b + b2 = 0 + -0.01785714286 Combine like terms: 0.01785714286 + -0.01785714286 = 0.00000000000 0.00000000000 + 0.01785714286b + b2 = 0 + -0.01785714286 0.01785714286b + b2 = 0 + -0.01785714286 Combine like terms: 0 + -0.01785714286 = -0.01785714286 0.01785714286b + b2 = -0.01785714286 The b term is b. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.01785714286b + 0.25 + b2 = -0.01785714286 + 0.25 Reorder the terms: 0.25 + 0.01785714286b + b2 = -0.01785714286 + 0.25 Combine like terms: -0.01785714286 + 0.25 = 0.23214285714 0.25 + 0.01785714286b + b2 = 0.23214285714 Factor a perfect square on the left side: (b + 0.5)(b + 0.5) = 0.23214285714 Calculate the square root of the right side: 0.481812056 Break this problem into two subproblems by setting (b + 0.5) equal to 0.481812056 and -0.481812056.Subproblem 1
b + 0.5 = 0.481812056 Simplifying b + 0.5 = 0.481812056 Reorder the terms: 0.5 + b = 0.481812056 Solving 0.5 + b = 0.481812056 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + b = 0.481812056 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = 0.481812056 + -0.5 b = 0.481812056 + -0.5 Combine like terms: 0.481812056 + -0.5 = -0.018187944 b = -0.018187944 Simplifying b = -0.018187944Subproblem 2
b + 0.5 = -0.481812056 Simplifying b + 0.5 = -0.481812056 Reorder the terms: 0.5 + b = -0.481812056 Solving 0.5 + b = -0.481812056 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + b = -0.481812056 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = -0.481812056 + -0.5 b = -0.481812056 + -0.5 Combine like terms: -0.481812056 + -0.5 = -0.981812056 b = -0.981812056 Simplifying b = -0.981812056Solution
The solution to the problem is based on the solutions from the subproblems. b = {-0.018187944, -0.981812056}
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