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Simplifying b2 + 14b + -31 = 0 Reorder the terms: -31 + 14b + b2 = 0 Solving -31 + 14b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '31' to each side of the equation. -31 + 14b + 31 + b2 = 0 + 31 Reorder the terms: -31 + 31 + 14b + b2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + 14b + b2 = 0 + 31 14b + b2 = 0 + 31 Combine like terms: 0 + 31 = 31 14b + b2 = 31 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 = 31 + 49 Reorder the terms: 49 + 14b + b2 = 31 + 49 Combine like terms: 31 + 49 = 80 49 + 14b + b2 = 80 Factor a perfect square on the left side: (b + 7)(b + 7) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (b + 7) equal to 8.94427191 and -8.94427191.Subproblem 1
b + 7 = 8.94427191 Simplifying b + 7 = 8.94427191 Reorder the terms: 7 + b = 8.94427191 Solving 7 + b = 8.94427191 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 = 8.94427191 + -7 Combine like terms: 7 + -7 = 0 0 + b = 8.94427191 + -7 b = 8.94427191 + -7 Combine like terms: 8.94427191 + -7 = 1.94427191 b = 1.94427191 Simplifying b = 1.94427191Subproblem 2
b + 7 = -8.94427191 Simplifying b + 7 = -8.94427191 Reorder the terms: 7 + b = -8.94427191 Solving 7 + b = -8.94427191 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 = -8.94427191 + -7 Combine like terms: 7 + -7 = 0 0 + b = -8.94427191 + -7 b = -8.94427191 + -7 Combine like terms: -8.94427191 + -7 = -15.94427191 b = -15.94427191 Simplifying b = -15.94427191Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.94427191, -15.94427191}
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