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Simplifying 2b2 + -1b = 43 Reorder the terms: -1b + 2b2 = 43 Solving -1b + 2b2 = 43 Solving for variable 'b'. Reorder the terms: -43 + -1b + 2b2 = 43 + -43 Combine like terms: 43 + -43 = 0 -43 + -1b + 2b2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -21.5 + -0.5b + b2 = 0 Move the constant term to the right: Add '21.5' to each side of the equation. -21.5 + -0.5b + 21.5 + b2 = 0 + 21.5 Reorder the terms: -21.5 + 21.5 + -0.5b + b2 = 0 + 21.5 Combine like terms: -21.5 + 21.5 = 0.0 0.0 + -0.5b + b2 = 0 + 21.5 -0.5b + b2 = 0 + 21.5 Combine like terms: 0 + 21.5 = 21.5 -0.5b + b2 = 21.5 The b term is -0.5b. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5b + 0.0625 + b2 = 21.5 + 0.0625 Reorder the terms: 0.0625 + -0.5b + b2 = 21.5 + 0.0625 Combine like terms: 21.5 + 0.0625 = 21.5625 0.0625 + -0.5b + b2 = 21.5625 Factor a perfect square on the left side: (b + -0.25)(b + -0.25) = 21.5625 Calculate the square root of the right side: 4.643543905 Break this problem into two subproblems by setting (b + -0.25) equal to 4.643543905 and -4.643543905.Subproblem 1
b + -0.25 = 4.643543905 Simplifying b + -0.25 = 4.643543905 Reorder the terms: -0.25 + b = 4.643543905 Solving -0.25 + b = 4.643543905 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + b = 4.643543905 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + b = 4.643543905 + 0.25 b = 4.643543905 + 0.25 Combine like terms: 4.643543905 + 0.25 = 4.893543905 b = 4.893543905 Simplifying b = 4.893543905Subproblem 2
b + -0.25 = -4.643543905 Simplifying b + -0.25 = -4.643543905 Reorder the terms: -0.25 + b = -4.643543905 Solving -0.25 + b = -4.643543905 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + b = -4.643543905 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + b = -4.643543905 + 0.25 b = -4.643543905 + 0.25 Combine like terms: -4.643543905 + 0.25 = -4.393543905 b = -4.393543905 Simplifying b = -4.393543905Solution
The solution to the problem is based on the solutions from the subproblems. b = {4.893543905, -4.393543905}
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