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Simplifying b2 + -11b = 24 Reorder the terms: -11b + b2 = 24 Solving -11b + b2 = 24 Solving for variable 'b'. Reorder the terms: -24 + -11b + b2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + -11b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + -11b + 24 + b2 = 0 + 24 Reorder the terms: -24 + 24 + -11b + b2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -11b + b2 = 0 + 24 -11b + b2 = 0 + 24 Combine like terms: 0 + 24 = 24 -11b + b2 = 24 The b term is -11b. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11b + 30.25 + b2 = 24 + 30.25 Reorder the terms: 30.25 + -11b + b2 = 24 + 30.25 Combine like terms: 24 + 30.25 = 54.25 30.25 + -11b + b2 = 54.25 Factor a perfect square on the left side: (b + -5.5)(b + -5.5) = 54.25 Calculate the square root of the right side: 7.365459931 Break this problem into two subproblems by setting (b + -5.5) equal to 7.365459931 and -7.365459931.Subproblem 1
b + -5.5 = 7.365459931 Simplifying b + -5.5 = 7.365459931 Reorder the terms: -5.5 + b = 7.365459931 Solving -5.5 + b = 7.365459931 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + b = 7.365459931 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + b = 7.365459931 + 5.5 b = 7.365459931 + 5.5 Combine like terms: 7.365459931 + 5.5 = 12.865459931 b = 12.865459931 Simplifying b = 12.865459931Subproblem 2
b + -5.5 = -7.365459931 Simplifying b + -5.5 = -7.365459931 Reorder the terms: -5.5 + b = -7.365459931 Solving -5.5 + b = -7.365459931 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + b = -7.365459931 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + b = -7.365459931 + 5.5 b = -7.365459931 + 5.5 Combine like terms: -7.365459931 + 5.5 = -1.865459931 b = -1.865459931 Simplifying b = -1.865459931Solution
The solution to the problem is based on the solutions from the subproblems. b = {12.865459931, -1.865459931}
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