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Simplifying b2 + 5b + -48 = 0 Reorder the terms: -48 + 5b + b2 = 0 Solving -48 + 5b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + 5b + 48 + b2 = 0 + 48 Reorder the terms: -48 + 48 + 5b + b2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 5b + b2 = 0 + 48 5b + b2 = 0 + 48 Combine like terms: 0 + 48 = 48 5b + b2 = 48 The b term is 5b. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5b + 6.25 + b2 = 48 + 6.25 Reorder the terms: 6.25 + 5b + b2 = 48 + 6.25 Combine like terms: 48 + 6.25 = 54.25 6.25 + 5b + b2 = 54.25 Factor a perfect square on the left side: (b + 2.5)(b + 2.5) = 54.25 Calculate the square root of the right side: 7.365459931 Break this problem into two subproblems by setting (b + 2.5) equal to 7.365459931 and -7.365459931.Subproblem 1
b + 2.5 = 7.365459931 Simplifying b + 2.5 = 7.365459931 Reorder the terms: 2.5 + b = 7.365459931 Solving 2.5 + b = 7.365459931 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + b = 7.365459931 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + b = 7.365459931 + -2.5 b = 7.365459931 + -2.5 Combine like terms: 7.365459931 + -2.5 = 4.865459931 b = 4.865459931 Simplifying b = 4.865459931Subproblem 2
b + 2.5 = -7.365459931 Simplifying b + 2.5 = -7.365459931 Reorder the terms: 2.5 + b = -7.365459931 Solving 2.5 + b = -7.365459931 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + b = -7.365459931 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + b = -7.365459931 + -2.5 b = -7.365459931 + -2.5 Combine like terms: -7.365459931 + -2.5 = -9.865459931 b = -9.865459931 Simplifying b = -9.865459931Solution
The solution to the problem is based on the solutions from the subproblems. b = {4.865459931, -9.865459931}
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