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Simplifying b2 + 2b + -48 = 8 Reorder the terms: -48 + 2b + b2 = 8 Solving -48 + 2b + b2 = 8 Solving for variable 'b'. Reorder the terms: -48 + -8 + 2b + b2 = 8 + -8 Combine like terms: -48 + -8 = -56 -56 + 2b + b2 = 8 + -8 Combine like terms: 8 + -8 = 0 -56 + 2b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + 2b + 56 + b2 = 0 + 56 Reorder the terms: -56 + 56 + 2b + b2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + 2b + b2 = 0 + 56 2b + b2 = 0 + 56 Combine like terms: 0 + 56 = 56 2b + b2 = 56 The b term is 2b. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2b + 1 + b2 = 56 + 1 Reorder the terms: 1 + 2b + b2 = 56 + 1 Combine like terms: 56 + 1 = 57 1 + 2b + b2 = 57 Factor a perfect square on the left side: (b + 1)(b + 1) = 57 Calculate the square root of the right side: 7.549834435 Break this problem into two subproblems by setting (b + 1) equal to 7.549834435 and -7.549834435.Subproblem 1
b + 1 = 7.549834435 Simplifying b + 1 = 7.549834435 Reorder the terms: 1 + b = 7.549834435 Solving 1 + b = 7.549834435 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + b = 7.549834435 + -1 Combine like terms: 1 + -1 = 0 0 + b = 7.549834435 + -1 b = 7.549834435 + -1 Combine like terms: 7.549834435 + -1 = 6.549834435 b = 6.549834435 Simplifying b = 6.549834435Subproblem 2
b + 1 = -7.549834435 Simplifying b + 1 = -7.549834435 Reorder the terms: 1 + b = -7.549834435 Solving 1 + b = -7.549834435 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + b = -7.549834435 + -1 Combine like terms: 1 + -1 = 0 0 + b = -7.549834435 + -1 b = -7.549834435 + -1 Combine like terms: -7.549834435 + -1 = -8.549834435 b = -8.549834435 Simplifying b = -8.549834435Solution
The solution to the problem is based on the solutions from the subproblems. b = {6.549834435, -8.549834435}
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