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Simplifying b + b2 = 68 Solving b + b2 = 68 Solving for variable 'b'. Reorder the terms: -68 + b + b2 = 68 + -68 Combine like terms: 68 + -68 = 0 -68 + b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '68' to each side of the equation. -68 + b + 68 + b2 = 0 + 68 Reorder the terms: -68 + 68 + b + b2 = 0 + 68 Combine like terms: -68 + 68 = 0 0 + b + b2 = 0 + 68 b + b2 = 0 + 68 Combine like terms: 0 + 68 = 68 b + b2 = 68 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. b + 0.25 + b2 = 68 + 0.25 Reorder the terms: 0.25 + b + b2 = 68 + 0.25 Combine like terms: 68 + 0.25 = 68.25 0.25 + b + b2 = 68.25 Factor a perfect square on the left side: (b + 0.5)(b + 0.5) = 68.25 Calculate the square root of the right side: 8.261355821 Break this problem into two subproblems by setting (b + 0.5) equal to 8.261355821 and -8.261355821.Subproblem 1
b + 0.5 = 8.261355821 Simplifying b + 0.5 = 8.261355821 Reorder the terms: 0.5 + b = 8.261355821 Solving 0.5 + b = 8.261355821 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 = 8.261355821 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = 8.261355821 + -0.5 b = 8.261355821 + -0.5 Combine like terms: 8.261355821 + -0.5 = 7.761355821 b = 7.761355821 Simplifying b = 7.761355821Subproblem 2
b + 0.5 = -8.261355821 Simplifying b + 0.5 = -8.261355821 Reorder the terms: 0.5 + b = -8.261355821 Solving 0.5 + b = -8.261355821 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 = -8.261355821 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = -8.261355821 + -0.5 b = -8.261355821 + -0.5 Combine like terms: -8.261355821 + -0.5 = -8.761355821 b = -8.761355821 Simplifying b = -8.761355821Solution
The solution to the problem is based on the solutions from the subproblems. b = {7.761355821, -8.761355821}
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