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Simplifying 0 = b4 + 0.9549296586b2 + -2.735671958 Reorder the terms: 0 = -2.735671958 + 0.9549296586b2 + b4 Solving 0 = -2.735671958 + 0.9549296586b2 + b4 Solving for variable 'b'. Combine like terms: 0 + 2.735671958 = 2.735671958 2.735671958 + -0.9549296586b2 + -1b4 = -2.735671958 + 0.9549296586b2 + b4 + 2.735671958 + -0.9549296586b2 + -1b4 Reorder the terms: 2.735671958 + -0.9549296586b2 + -1b4 = -2.735671958 + 2.735671958 + 0.9549296586b2 + -0.9549296586b2 + b4 + -1b4 Combine like terms: -2.735671958 + 2.735671958 = 0.000000000 2.735671958 + -0.9549296586b2 + -1b4 = 0.000000000 + 0.9549296586b2 + -0.9549296586b2 + b4 + -1b4 2.735671958 + -0.9549296586b2 + -1b4 = 0.9549296586b2 + -0.9549296586b2 + b4 + -1b4 Combine like terms: 0.9549296586b2 + -0.9549296586b2 = 0.0000000000 2.735671958 + -0.9549296586b2 + -1b4 = 0.0000000000 + b4 + -1b4 2.735671958 + -0.9549296586b2 + -1b4 = b4 + -1b4 Combine like terms: b4 + -1b4 = 0 2.735671958 + -0.9549296586b2 + -1b4 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2.735671958 + 0.9549296586b2 + b4 = 0 Move the constant term to the right: Add '2.735671958' to each side of the equation. -2.735671958 + 0.9549296586b2 + 2.735671958 + b4 = 0 + 2.735671958 Reorder the terms: -2.735671958 + 2.735671958 + 0.9549296586b2 + b4 = 0 + 2.735671958 Combine like terms: -2.735671958 + 2.735671958 = 0.000000000 0.000000000 + 0.9549296586b2 + b4 = 0 + 2.735671958 0.9549296586b2 + b4 = 0 + 2.735671958 Combine like terms: 0 + 2.735671958 = 2.735671958 0.9549296586b2 + b4 = 2.735671958 The b term is 0.9549296586b2. Take half its coefficient (0.4774648293). Square it (0.2279726632) and add it to both sides. Add '0.2279726632' to each side of the equation. 0.9549296586b2 + 0.2279726632 + b4 = 2.735671958 + 0.2279726632 Reorder the terms: 0.2279726632 + 0.9549296586b2 + b4 = 2.735671958 + 0.2279726632 Combine like terms: 2.735671958 + 0.2279726632 = 2.9636446212 0.2279726632 + 0.9549296586b2 + b4 = 2.9636446212 Factor a perfect square on the left side: (b2 + 0.4774648293)(b2 + 0.4774648293) = 2.9636446212 Calculate the square root of the right side: 1.721523924 Break this problem into two subproblems by setting (b2 + 0.4774648293) equal to 1.721523924 and -1.721523924.Subproblem 1
b2 + 0.4774648293 = 1.721523924 Simplifying b2 + 0.4774648293 = 1.721523924 Reorder the terms: 0.4774648293 + b2 = 1.721523924 Solving 0.4774648293 + b2 = 1.721523924 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.4774648293' to each side of the equation. 0.4774648293 + -0.4774648293 + b2 = 1.721523924 + -0.4774648293 Combine like terms: 0.4774648293 + -0.4774648293 = 0.0000000000 0.0000000000 + b2 = 1.721523924 + -0.4774648293 b2 = 1.721523924 + -0.4774648293 Combine like terms: 1.721523924 + -0.4774648293 = 1.2440590947 b2 = 1.2440590947 Simplifying b2 = 1.2440590947 Take the square root of each side: b = {-1.115373971, 1.115373971}Subproblem 2
b2 + 0.4774648293 = -1.721523924 Simplifying b2 + 0.4774648293 = -1.721523924 Reorder the terms: 0.4774648293 + b2 = -1.721523924 Solving 0.4774648293 + b2 = -1.721523924 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.4774648293' to each side of the equation. 0.4774648293 + -0.4774648293 + b2 = -1.721523924 + -0.4774648293 Combine like terms: 0.4774648293 + -0.4774648293 = 0.0000000000 0.0000000000 + b2 = -1.721523924 + -0.4774648293 b2 = -1.721523924 + -0.4774648293 Combine like terms: -1.721523924 + -0.4774648293 = -2.1989887533 b2 = -2.1989887533 Simplifying b2 = -2.1989887533 Reorder the terms: 2.1989887533 + b2 = -2.1989887533 + 2.1989887533 Combine like terms: -2.1989887533 + 2.1989887533 = 0.0000000000 2.1989887533 + b2 = 0.0000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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