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Simplifying 59b2 + b = 1 Reorder the terms: b + 59b2 = 1 Solving b + 59b2 = 1 Solving for variable 'b'. Reorder the terms: -1 + b + 59b2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + b + 59b2 = 0 Begin completing the square. Divide all terms by 59 the coefficient of the squared term: Divide each side by '59'. -0.01694915254 + 0.01694915254b + b2 = 0 Move the constant term to the right: Add '0.01694915254' to each side of the equation. -0.01694915254 + 0.01694915254b + 0.01694915254 + b2 = 0 + 0.01694915254 Reorder the terms: -0.01694915254 + 0.01694915254 + 0.01694915254b + b2 = 0 + 0.01694915254 Combine like terms: -0.01694915254 + 0.01694915254 = 0.00000000000 0.00000000000 + 0.01694915254b + b2 = 0 + 0.01694915254 0.01694915254b + b2 = 0 + 0.01694915254 Combine like terms: 0 + 0.01694915254 = 0.01694915254 0.01694915254b + b2 = 0.01694915254 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. 0.01694915254b + 0.25 + b2 = 0.01694915254 + 0.25 Reorder the terms: 0.25 + 0.01694915254b + b2 = 0.01694915254 + 0.25 Combine like terms: 0.01694915254 + 0.25 = 0.26694915254 0.25 + 0.01694915254b + b2 = 0.26694915254 Factor a perfect square on the left side: (b + 0.5)(b + 0.5) = 0.26694915254 Calculate the square root of the right side: 0.516671223 Break this problem into two subproblems by setting (b + 0.5) equal to 0.516671223 and -0.516671223.Subproblem 1
b + 0.5 = 0.516671223 Simplifying b + 0.5 = 0.516671223 Reorder the terms: 0.5 + b = 0.516671223 Solving 0.5 + b = 0.516671223 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 = 0.516671223 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = 0.516671223 + -0.5 b = 0.516671223 + -0.5 Combine like terms: 0.516671223 + -0.5 = 0.016671223 b = 0.016671223 Simplifying b = 0.016671223Subproblem 2
b + 0.5 = -0.516671223 Simplifying b + 0.5 = -0.516671223 Reorder the terms: 0.5 + b = -0.516671223 Solving 0.5 + b = -0.516671223 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 = -0.516671223 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = -0.516671223 + -0.5 b = -0.516671223 + -0.5 Combine like terms: -0.516671223 + -0.5 = -1.016671223 b = -1.016671223 Simplifying b = -1.016671223Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.016671223, -1.016671223}
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