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Simplifying b2 + 3b + -96.89 = 8.45 Reorder the terms: -96.89 + 3b + b2 = 8.45 Solving -96.89 + 3b + b2 = 8.45 Solving for variable 'b'. Reorder the terms: -96.89 + -8.45 + 3b + b2 = 8.45 + -8.45 Combine like terms: -96.89 + -8.45 = -105.34 -105.34 + 3b + b2 = 8.45 + -8.45 Combine like terms: 8.45 + -8.45 = 0.00 -105.34 + 3b + b2 = 0.00 Begin completing the square. Move the constant term to the right: Add '105.34' to each side of the equation. -105.34 + 3b + 105.34 + b2 = 0.00 + 105.34 Reorder the terms: -105.34 + 105.34 + 3b + b2 = 0.00 + 105.34 Combine like terms: -105.34 + 105.34 = 0.00 0.00 + 3b + b2 = 0.00 + 105.34 3b + b2 = 0.00 + 105.34 Combine like terms: 0.00 + 105.34 = 105.34 3b + b2 = 105.34 The b term is 3b. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3b + 2.25 + b2 = 105.34 + 2.25 Reorder the terms: 2.25 + 3b + b2 = 105.34 + 2.25 Combine like terms: 105.34 + 2.25 = 107.59 2.25 + 3b + b2 = 107.59 Factor a perfect square on the left side: (b + 1.5)(b + 1.5) = 107.59 Calculate the square root of the right side: 10.372559954 Break this problem into two subproblems by setting (b + 1.5) equal to 10.372559954 and -10.372559954.Subproblem 1
b + 1.5 = 10.372559954 Simplifying b + 1.5 = 10.372559954 Reorder the terms: 1.5 + b = 10.372559954 Solving 1.5 + b = 10.372559954 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + b = 10.372559954 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + b = 10.372559954 + -1.5 b = 10.372559954 + -1.5 Combine like terms: 10.372559954 + -1.5 = 8.872559954 b = 8.872559954 Simplifying b = 8.872559954Subproblem 2
b + 1.5 = -10.372559954 Simplifying b + 1.5 = -10.372559954 Reorder the terms: 1.5 + b = -10.372559954 Solving 1.5 + b = -10.372559954 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + b = -10.372559954 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + b = -10.372559954 + -1.5 b = -10.372559954 + -1.5 Combine like terms: -10.372559954 + -1.5 = -11.872559954 b = -11.872559954 Simplifying b = -11.872559954Solution
The solution to the problem is based on the solutions from the subproblems. b = {8.872559954, -11.872559954}
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