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Simplifying b2 + -7b = 17 Reorder the terms: -7b + b2 = 17 Solving -7b + b2 = 17 Solving for variable 'b'. Reorder the terms: -17 + -7b + b2 = 17 + -17 Combine like terms: 17 + -17 = 0 -17 + -7b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + -7b + 17 + b2 = 0 + 17 Reorder the terms: -17 + 17 + -7b + b2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -7b + b2 = 0 + 17 -7b + b2 = 0 + 17 Combine like terms: 0 + 17 = 17 -7b + b2 = 17 The b term is -7b. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7b + 12.25 + b2 = 17 + 12.25 Reorder the terms: 12.25 + -7b + b2 = 17 + 12.25 Combine like terms: 17 + 12.25 = 29.25 12.25 + -7b + b2 = 29.25 Factor a perfect square on the left side: (b + -3.5)(b + -3.5) = 29.25 Calculate the square root of the right side: 5.408326913 Break this problem into two subproblems by setting (b + -3.5) equal to 5.408326913 and -5.408326913.Subproblem 1
b + -3.5 = 5.408326913 Simplifying b + -3.5 = 5.408326913 Reorder the terms: -3.5 + b = 5.408326913 Solving -3.5 + b = 5.408326913 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + b = 5.408326913 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + b = 5.408326913 + 3.5 b = 5.408326913 + 3.5 Combine like terms: 5.408326913 + 3.5 = 8.908326913 b = 8.908326913 Simplifying b = 8.908326913Subproblem 2
b + -3.5 = -5.408326913 Simplifying b + -3.5 = -5.408326913 Reorder the terms: -3.5 + b = -5.408326913 Solving -3.5 + b = -5.408326913 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + b = -5.408326913 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + b = -5.408326913 + 3.5 b = -5.408326913 + 3.5 Combine like terms: -5.408326913 + 3.5 = -1.908326913 b = -1.908326913 Simplifying b = -1.908326913Solution
The solution to the problem is based on the solutions from the subproblems. b = {8.908326913, -1.908326913}
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