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Simplifying 293b + -1b2 = 1876 Solving 293b + -1b2 = 1876 Solving for variable 'b'. Reorder the terms: -1876 + 293b + -1b2 = 1876 + -1876 Combine like terms: 1876 + -1876 = 0 -1876 + 293b + -1b2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1876 + -293b + b2 = 0 Move the constant term to the right: Add '-1876' to each side of the equation. 1876 + -293b + -1876 + b2 = 0 + -1876 Reorder the terms: 1876 + -1876 + -293b + b2 = 0 + -1876 Combine like terms: 1876 + -1876 = 0 0 + -293b + b2 = 0 + -1876 -293b + b2 = 0 + -1876 Combine like terms: 0 + -1876 = -1876 -293b + b2 = -1876 The b term is -293b. Take half its coefficient (-146.5). Square it (21462.25) and add it to both sides. Add '21462.25' to each side of the equation. -293b + 21462.25 + b2 = -1876 + 21462.25 Reorder the terms: 21462.25 + -293b + b2 = -1876 + 21462.25 Combine like terms: -1876 + 21462.25 = 19586.25 21462.25 + -293b + b2 = 19586.25 Factor a perfect square on the left side: (b + -146.5)(b + -146.5) = 19586.25 Calculate the square root of the right side: 139.950884242 Break this problem into two subproblems by setting (b + -146.5) equal to 139.950884242 and -139.950884242.Subproblem 1
b + -146.5 = 139.950884242 Simplifying b + -146.5 = 139.950884242 Reorder the terms: -146.5 + b = 139.950884242 Solving -146.5 + b = 139.950884242 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '146.5' to each side of the equation. -146.5 + 146.5 + b = 139.950884242 + 146.5 Combine like terms: -146.5 + 146.5 = 0.0 0.0 + b = 139.950884242 + 146.5 b = 139.950884242 + 146.5 Combine like terms: 139.950884242 + 146.5 = 286.450884242 b = 286.450884242 Simplifying b = 286.450884242Subproblem 2
b + -146.5 = -139.950884242 Simplifying b + -146.5 = -139.950884242 Reorder the terms: -146.5 + b = -139.950884242 Solving -146.5 + b = -139.950884242 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '146.5' to each side of the equation. -146.5 + 146.5 + b = -139.950884242 + 146.5 Combine like terms: -146.5 + 146.5 = 0.0 0.0 + b = -139.950884242 + 146.5 b = -139.950884242 + 146.5 Combine like terms: -139.950884242 + 146.5 = 6.549115758 b = 6.549115758 Simplifying b = 6.549115758Solution
The solution to the problem is based on the solutions from the subproblems. b = {286.450884242, 6.549115758}
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