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Simplifying b + (b2 + -2) + (b2 + -2 + 2) = 60 Reorder the terms: b + (-2 + b2) + (b2 + -2 + 2) = 60 Remove parenthesis around (-2 + b2) b + -2 + b2 + (b2 + -2 + 2) = 60 Reorder the terms: b + -2 + b2 + (-2 + 2 + b2) = 60 Combine like terms: -2 + 2 = 0 b + -2 + b2 + (0 + b2) = 60 b + -2 + b2 + (b2) = 60 b + -2 + b2 + b2 = 60 Reorder the terms: -2 + b + b2 + b2 = 60 Combine like terms: b2 + b2 = 2b2 -2 + b + 2b2 = 60 Solving -2 + b + 2b2 = 60 Solving for variable 'b'. Reorder the terms: -2 + -60 + b + 2b2 = 60 + -60 Combine like terms: -2 + -60 = -62 -62 + b + 2b2 = 60 + -60 Combine like terms: 60 + -60 = 0 -62 + b + 2b2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -31 + 0.5b + b2 = 0 Move the constant term to the right: Add '31' to each side of the equation. -31 + 0.5b + 31 + b2 = 0 + 31 Reorder the terms: -31 + 31 + 0.5b + b2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + 0.5b + b2 = 0 + 31 0.5b + b2 = 0 + 31 Combine like terms: 0 + 31 = 31 0.5b + b2 = 31 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. 0.5b + 0.25 + b2 = 31 + 0.25 Reorder the terms: 0.25 + 0.5b + b2 = 31 + 0.25 Combine like terms: 31 + 0.25 = 31.25 0.25 + 0.5b + b2 = 31.25 Factor a perfect square on the left side: (b + 0.5)(b + 0.5) = 31.25 Calculate the square root of the right side: 5.590169944 Break this problem into two subproblems by setting (b + 0.5) equal to 5.590169944 and -5.590169944.Subproblem 1
b + 0.5 = 5.590169944 Simplifying b + 0.5 = 5.590169944 Reorder the terms: 0.5 + b = 5.590169944 Solving 0.5 + b = 5.590169944 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 = 5.590169944 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = 5.590169944 + -0.5 b = 5.590169944 + -0.5 Combine like terms: 5.590169944 + -0.5 = 5.090169944 b = 5.090169944 Simplifying b = 5.090169944Subproblem 2
b + 0.5 = -5.590169944 Simplifying b + 0.5 = -5.590169944 Reorder the terms: 0.5 + b = -5.590169944 Solving 0.5 + b = -5.590169944 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 = -5.590169944 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = -5.590169944 + -0.5 b = -5.590169944 + -0.5 Combine like terms: -5.590169944 + -0.5 = -6.090169944 b = -6.090169944 Simplifying b = -6.090169944Solution
The solution to the problem is based on the solutions from the subproblems. b = {5.090169944, -6.090169944}
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