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Simplifying b2 + 250b = 1225 Reorder the terms: 250b + b2 = 1225 Solving 250b + b2 = 1225 Solving for variable 'b'. Reorder the terms: -1225 + 250b + b2 = 1225 + -1225 Combine like terms: 1225 + -1225 = 0 -1225 + 250b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '1225' to each side of the equation. -1225 + 250b + 1225 + b2 = 0 + 1225 Reorder the terms: -1225 + 1225 + 250b + b2 = 0 + 1225 Combine like terms: -1225 + 1225 = 0 0 + 250b + b2 = 0 + 1225 250b + b2 = 0 + 1225 Combine like terms: 0 + 1225 = 1225 250b + b2 = 1225 The b term is 250b. Take half its coefficient (125). Square it (15625) and add it to both sides. Add '15625' to each side of the equation. 250b + 15625 + b2 = 1225 + 15625 Reorder the terms: 15625 + 250b + b2 = 1225 + 15625 Combine like terms: 1225 + 15625 = 16850 15625 + 250b + b2 = 16850 Factor a perfect square on the left side: (b + 125)(b + 125) = 16850 Calculate the square root of the right side: 129.807549857 Break this problem into two subproblems by setting (b + 125) equal to 129.807549857 and -129.807549857.Subproblem 1
b + 125 = 129.807549857 Simplifying b + 125 = 129.807549857 Reorder the terms: 125 + b = 129.807549857 Solving 125 + b = 129.807549857 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-125' to each side of the equation. 125 + -125 + b = 129.807549857 + -125 Combine like terms: 125 + -125 = 0 0 + b = 129.807549857 + -125 b = 129.807549857 + -125 Combine like terms: 129.807549857 + -125 = 4.807549857 b = 4.807549857 Simplifying b = 4.807549857Subproblem 2
b + 125 = -129.807549857 Simplifying b + 125 = -129.807549857 Reorder the terms: 125 + b = -129.807549857 Solving 125 + b = -129.807549857 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-125' to each side of the equation. 125 + -125 + b = -129.807549857 + -125 Combine like terms: 125 + -125 = 0 0 + b = -129.807549857 + -125 b = -129.807549857 + -125 Combine like terms: -129.807549857 + -125 = -254.807549857 b = -254.807549857 Simplifying b = -254.807549857Solution
The solution to the problem is based on the solutions from the subproblems. b = {4.807549857, -254.807549857}
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