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Simplifying 4b2 + 9b + -29 = 0 Reorder the terms: -29 + 9b + 4b2 = 0 Solving -29 + 9b + 4b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -7.25 + 2.25b + b2 = 0 Move the constant term to the right: Add '7.25' to each side of the equation. -7.25 + 2.25b + 7.25 + b2 = 0 + 7.25 Reorder the terms: -7.25 + 7.25 + 2.25b + b2 = 0 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + 2.25b + b2 = 0 + 7.25 2.25b + b2 = 0 + 7.25 Combine like terms: 0 + 7.25 = 7.25 2.25b + b2 = 7.25 The b term is 2.25b. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25b + 1.265625 + b2 = 7.25 + 1.265625 Reorder the terms: 1.265625 + 2.25b + b2 = 7.25 + 1.265625 Combine like terms: 7.25 + 1.265625 = 8.515625 1.265625 + 2.25b + b2 = 8.515625 Factor a perfect square on the left side: (b + 1.125)(b + 1.125) = 8.515625 Calculate the square root of the right side: 2.918154382 Break this problem into two subproblems by setting (b + 1.125) equal to 2.918154382 and -2.918154382.Subproblem 1
b + 1.125 = 2.918154382 Simplifying b + 1.125 = 2.918154382 Reorder the terms: 1.125 + b = 2.918154382 Solving 1.125 + b = 2.918154382 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + b = 2.918154382 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + b = 2.918154382 + -1.125 b = 2.918154382 + -1.125 Combine like terms: 2.918154382 + -1.125 = 1.793154382 b = 1.793154382 Simplifying b = 1.793154382Subproblem 2
b + 1.125 = -2.918154382 Simplifying b + 1.125 = -2.918154382 Reorder the terms: 1.125 + b = -2.918154382 Solving 1.125 + b = -2.918154382 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + b = -2.918154382 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + b = -2.918154382 + -1.125 b = -2.918154382 + -1.125 Combine like terms: -2.918154382 + -1.125 = -4.043154382 b = -4.043154382 Simplifying b = -4.043154382Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.793154382, -4.043154382}
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