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Simplifying b2 + 73b = 146 Reorder the terms: 73b + b2 = 146 Solving 73b + b2 = 146 Solving for variable 'b'. Reorder the terms: -146 + 73b + b2 = 146 + -146 Combine like terms: 146 + -146 = 0 -146 + 73b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '146' to each side of the equation. -146 + 73b + 146 + b2 = 0 + 146 Reorder the terms: -146 + 146 + 73b + b2 = 0 + 146 Combine like terms: -146 + 146 = 0 0 + 73b + b2 = 0 + 146 73b + b2 = 0 + 146 Combine like terms: 0 + 146 = 146 73b + b2 = 146 The b term is 73b. Take half its coefficient (36.5). Square it (1332.25) and add it to both sides. Add '1332.25' to each side of the equation. 73b + 1332.25 + b2 = 146 + 1332.25 Reorder the terms: 1332.25 + 73b + b2 = 146 + 1332.25 Combine like terms: 146 + 1332.25 = 1478.25 1332.25 + 73b + b2 = 1478.25 Factor a perfect square on the left side: (b + 36.5)(b + 36.5) = 1478.25 Calculate the square root of the right side: 38.448016854 Break this problem into two subproblems by setting (b + 36.5) equal to 38.448016854 and -38.448016854.Subproblem 1
b + 36.5 = 38.448016854 Simplifying b + 36.5 = 38.448016854 Reorder the terms: 36.5 + b = 38.448016854 Solving 36.5 + b = 38.448016854 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-36.5' to each side of the equation. 36.5 + -36.5 + b = 38.448016854 + -36.5 Combine like terms: 36.5 + -36.5 = 0.0 0.0 + b = 38.448016854 + -36.5 b = 38.448016854 + -36.5 Combine like terms: 38.448016854 + -36.5 = 1.948016854 b = 1.948016854 Simplifying b = 1.948016854Subproblem 2
b + 36.5 = -38.448016854 Simplifying b + 36.5 = -38.448016854 Reorder the terms: 36.5 + b = -38.448016854 Solving 36.5 + b = -38.448016854 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-36.5' to each side of the equation. 36.5 + -36.5 + b = -38.448016854 + -36.5 Combine like terms: 36.5 + -36.5 = 0.0 0.0 + b = -38.448016854 + -36.5 b = -38.448016854 + -36.5 Combine like terms: -38.448016854 + -36.5 = -74.948016854 b = -74.948016854 Simplifying b = -74.948016854Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.948016854, -74.948016854}
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