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Simplifying 4b2 + -1b + -34 + 0 = 0 Reorder the terms: -34 + 0 + -1b + 4b2 = 0 Combine like terms: -34 + 0 = -34 -34 + -1b + 4b2 = 0 Solving -34 + -1b + 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'. -8.5 + -0.25b + b2 = 0 Move the constant term to the right: Add '8.5' to each side of the equation. -8.5 + -0.25b + 8.5 + b2 = 0 + 8.5 Reorder the terms: -8.5 + 8.5 + -0.25b + b2 = 0 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + -0.25b + b2 = 0 + 8.5 -0.25b + b2 = 0 + 8.5 Combine like terms: 0 + 8.5 = 8.5 -0.25b + b2 = 8.5 The b term is -0.25b. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25b + 0.015625 + b2 = 8.5 + 0.015625 Reorder the terms: 0.015625 + -0.25b + b2 = 8.5 + 0.015625 Combine like terms: 8.5 + 0.015625 = 8.515625 0.015625 + -0.25b + b2 = 8.515625 Factor a perfect square on the left side: (b + -0.125)(b + -0.125) = 8.515625 Calculate the square root of the right side: 2.918154382 Break this problem into two subproblems by setting (b + -0.125) equal to 2.918154382 and -2.918154382.Subproblem 1
b + -0.125 = 2.918154382 Simplifying b + -0.125 = 2.918154382 Reorder the terms: -0.125 + b = 2.918154382 Solving -0.125 + b = 2.918154382 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + b = 2.918154382 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + b = 2.918154382 + 0.125 b = 2.918154382 + 0.125 Combine like terms: 2.918154382 + 0.125 = 3.043154382 b = 3.043154382 Simplifying b = 3.043154382Subproblem 2
b + -0.125 = -2.918154382 Simplifying b + -0.125 = -2.918154382 Reorder the terms: -0.125 + b = -2.918154382 Solving -0.125 + b = -2.918154382 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + b = -2.918154382 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + b = -2.918154382 + 0.125 b = -2.918154382 + 0.125 Combine like terms: -2.918154382 + 0.125 = -2.793154382 b = -2.793154382 Simplifying b = -2.793154382Solution
The solution to the problem is based on the solutions from the subproblems. b = {3.043154382, -2.793154382}
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