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Simplifying b2 + -14b = -17 Reorder the terms: -14b + b2 = -17 Solving -14b + b2 = -17 Solving for variable 'b'. Reorder the terms: 17 + -14b + b2 = -17 + 17 Combine like terms: -17 + 17 = 0 17 + -14b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + -14b + -17 + b2 = 0 + -17 Reorder the terms: 17 + -17 + -14b + b2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -14b + b2 = 0 + -17 -14b + b2 = 0 + -17 Combine like terms: 0 + -17 = -17 -14b + b2 = -17 The b term is -14b. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14b + 49 + b2 = -17 + 49 Reorder the terms: 49 + -14b + b2 = -17 + 49 Combine like terms: -17 + 49 = 32 49 + -14b + b2 = 32 Factor a perfect square on the left side: (b + -7)(b + -7) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (b + -7) equal to 5.656854249 and -5.656854249.Subproblem 1
b + -7 = 5.656854249 Simplifying b + -7 = 5.656854249 Reorder the terms: -7 + b = 5.656854249 Solving -7 + b = 5.656854249 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + b = 5.656854249 + 7 Combine like terms: -7 + 7 = 0 0 + b = 5.656854249 + 7 b = 5.656854249 + 7 Combine like terms: 5.656854249 + 7 = 12.656854249 b = 12.656854249 Simplifying b = 12.656854249Subproblem 2
b + -7 = -5.656854249 Simplifying b + -7 = -5.656854249 Reorder the terms: -7 + b = -5.656854249 Solving -7 + b = -5.656854249 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + b = -5.656854249 + 7 Combine like terms: -7 + 7 = 0 0 + b = -5.656854249 + 7 b = -5.656854249 + 7 Combine like terms: -5.656854249 + 7 = 1.343145751 b = 1.343145751 Simplifying b = 1.343145751Solution
The solution to the problem is based on the solutions from the subproblems. b = {12.656854249, 1.343145751}
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