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Simplifying b(b + 450) = 575 Reorder the terms: b(450 + b) = 575 (450 * b + b * b) = 575 (450b + b2) = 575 Solving 450b + b2 = 575 Solving for variable 'b'. Reorder the terms: -575 + 450b + b2 = 575 + -575 Combine like terms: 575 + -575 = 0 -575 + 450b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '575' to each side of the equation. -575 + 450b + 575 + b2 = 0 + 575 Reorder the terms: -575 + 575 + 450b + b2 = 0 + 575 Combine like terms: -575 + 575 = 0 0 + 450b + b2 = 0 + 575 450b + b2 = 0 + 575 Combine like terms: 0 + 575 = 575 450b + b2 = 575 The b term is 450b. Take half its coefficient (225). Square it (50625) and add it to both sides. Add '50625' to each side of the equation. 450b + 50625 + b2 = 575 + 50625 Reorder the terms: 50625 + 450b + b2 = 575 + 50625 Combine like terms: 575 + 50625 = 51200 50625 + 450b + b2 = 51200 Factor a perfect square on the left side: (b + 225)(b + 225) = 51200 Calculate the square root of the right side: 226.27416998 Break this problem into two subproblems by setting (b + 225) equal to 226.27416998 and -226.27416998.Subproblem 1
b + 225 = 226.27416998 Simplifying b + 225 = 226.27416998 Reorder the terms: 225 + b = 226.27416998 Solving 225 + b = 226.27416998 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-225' to each side of the equation. 225 + -225 + b = 226.27416998 + -225 Combine like terms: 225 + -225 = 0 0 + b = 226.27416998 + -225 b = 226.27416998 + -225 Combine like terms: 226.27416998 + -225 = 1.27416998 b = 1.27416998 Simplifying b = 1.27416998Subproblem 2
b + 225 = -226.27416998 Simplifying b + 225 = -226.27416998 Reorder the terms: 225 + b = -226.27416998 Solving 225 + b = -226.27416998 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-225' to each side of the equation. 225 + -225 + b = -226.27416998 + -225 Combine like terms: 225 + -225 = 0 0 + b = -226.27416998 + -225 b = -226.27416998 + -225 Combine like terms: -226.27416998 + -225 = -451.27416998 b = -451.27416998 Simplifying b = -451.27416998Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.27416998, -451.27416998}
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