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Simplifying 20b = 1 + 4b2 Solving 20b = 1 + 4b2 Solving for variable 'b'. Reorder the terms: -1 + 20b + -4b2 = 1 + 4b2 + -1 + -4b2 Reorder the terms: -1 + 20b + -4b2 = 1 + -1 + 4b2 + -4b2 Combine like terms: 1 + -1 = 0 -1 + 20b + -4b2 = 0 + 4b2 + -4b2 -1 + 20b + -4b2 = 4b2 + -4b2 Combine like terms: 4b2 + -4b2 = 0 -1 + 20b + -4b2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 0.25 + -5b + b2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -5b + -0.25 + b2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -5b + b2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -5b + b2 = 0 + -0.25 -5b + b2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -5b + b2 = -0.25 The b term is -5b. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5b + 6.25 + b2 = -0.25 + 6.25 Reorder the terms: 6.25 + -5b + b2 = -0.25 + 6.25 Combine like terms: -0.25 + 6.25 = 6 6.25 + -5b + b2 = 6 Factor a perfect square on the left side: (b + -2.5)(b + -2.5) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (b + -2.5) equal to 2.449489743 and -2.449489743.Subproblem 1
b + -2.5 = 2.449489743 Simplifying b + -2.5 = 2.449489743 Reorder the terms: -2.5 + b = 2.449489743 Solving -2.5 + b = 2.449489743 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + b = 2.449489743 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + b = 2.449489743 + 2.5 b = 2.449489743 + 2.5 Combine like terms: 2.449489743 + 2.5 = 4.949489743 b = 4.949489743 Simplifying b = 4.949489743Subproblem 2
b + -2.5 = -2.449489743 Simplifying b + -2.5 = -2.449489743 Reorder the terms: -2.5 + b = -2.449489743 Solving -2.5 + b = -2.449489743 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + b = -2.449489743 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + b = -2.449489743 + 2.5 b = -2.449489743 + 2.5 Combine like terms: -2.449489743 + 2.5 = 0.050510257 b = 0.050510257 Simplifying b = 0.050510257Solution
The solution to the problem is based on the solutions from the subproblems. b = {4.949489743, 0.050510257}
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