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Simplifying (b + 10) * b = 5000 Reorder the terms: (10 + b) * b = 5000 Reorder the terms for easier multiplication: b(10 + b) = 5000 (10 * b + b * b) = 5000 (10b + b2) = 5000 Solving 10b + b2 = 5000 Solving for variable 'b'. Reorder the terms: -5000 + 10b + b2 = 5000 + -5000 Combine like terms: 5000 + -5000 = 0 -5000 + 10b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '5000' to each side of the equation. -5000 + 10b + 5000 + b2 = 0 + 5000 Reorder the terms: -5000 + 5000 + 10b + b2 = 0 + 5000 Combine like terms: -5000 + 5000 = 0 0 + 10b + b2 = 0 + 5000 10b + b2 = 0 + 5000 Combine like terms: 0 + 5000 = 5000 10b + b2 = 5000 The b term is 10b. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10b + 25 + b2 = 5000 + 25 Reorder the terms: 25 + 10b + b2 = 5000 + 25 Combine like terms: 5000 + 25 = 5025 25 + 10b + b2 = 5025 Factor a perfect square on the left side: (b + 5)(b + 5) = 5025 Calculate the square root of the right side: 70.887234394 Break this problem into two subproblems by setting (b + 5) equal to 70.887234394 and -70.887234394.Subproblem 1
b + 5 = 70.887234394 Simplifying b + 5 = 70.887234394 Reorder the terms: 5 + b = 70.887234394 Solving 5 + b = 70.887234394 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + b = 70.887234394 + -5 Combine like terms: 5 + -5 = 0 0 + b = 70.887234394 + -5 b = 70.887234394 + -5 Combine like terms: 70.887234394 + -5 = 65.887234394 b = 65.887234394 Simplifying b = 65.887234394Subproblem 2
b + 5 = -70.887234394 Simplifying b + 5 = -70.887234394 Reorder the terms: 5 + b = -70.887234394 Solving 5 + b = -70.887234394 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + b = -70.887234394 + -5 Combine like terms: 5 + -5 = 0 0 + b = -70.887234394 + -5 b = -70.887234394 + -5 Combine like terms: -70.887234394 + -5 = -75.887234394 b = -75.887234394 Simplifying b = -75.887234394Solution
The solution to the problem is based on the solutions from the subproblems. b = {65.887234394, -75.887234394}
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