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Simplifying b + b2 = 565 Solving b + b2 = 565 Solving for variable 'b'. Reorder the terms: -565 + b + b2 = 565 + -565 Combine like terms: 565 + -565 = 0 -565 + b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '565' to each side of the equation. -565 + b + 565 + b2 = 0 + 565 Reorder the terms: -565 + 565 + b + b2 = 0 + 565 Combine like terms: -565 + 565 = 0 0 + b + b2 = 0 + 565 b + b2 = 0 + 565 Combine like terms: 0 + 565 = 565 b + b2 = 565 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 = 565 + 0.25 Reorder the terms: 0.25 + b + b2 = 565 + 0.25 Combine like terms: 565 + 0.25 = 565.25 0.25 + b + b2 = 565.25 Factor a perfect square on the left side: (b + 0.5)(b + 0.5) = 565.25 Calculate the square root of the right side: 23.774986856 Break this problem into two subproblems by setting (b + 0.5) equal to 23.774986856 and -23.774986856.Subproblem 1
b + 0.5 = 23.774986856 Simplifying b + 0.5 = 23.774986856 Reorder the terms: 0.5 + b = 23.774986856 Solving 0.5 + b = 23.774986856 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 = 23.774986856 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = 23.774986856 + -0.5 b = 23.774986856 + -0.5 Combine like terms: 23.774986856 + -0.5 = 23.274986856 b = 23.274986856 Simplifying b = 23.274986856Subproblem 2
b + 0.5 = -23.774986856 Simplifying b + 0.5 = -23.774986856 Reorder the terms: 0.5 + b = -23.774986856 Solving 0.5 + b = -23.774986856 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 = -23.774986856 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = -23.774986856 + -0.5 b = -23.774986856 + -0.5 Combine like terms: -23.774986856 + -0.5 = -24.274986856 b = -24.274986856 Simplifying b = -24.274986856Solution
The solution to the problem is based on the solutions from the subproblems. b = {23.274986856, -24.274986856}
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