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Simplifying b2 = 14 + -15b Solving b2 = 14 + -15b Solving for variable 'b'. Reorder the terms: -14 + 15b + b2 = 14 + -15b + -14 + 15b Reorder the terms: -14 + 15b + b2 = 14 + -14 + -15b + 15b Combine like terms: 14 + -14 = 0 -14 + 15b + b2 = 0 + -15b + 15b -14 + 15b + b2 = -15b + 15b Combine like terms: -15b + 15b = 0 -14 + 15b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + 15b + 14 + b2 = 0 + 14 Reorder the terms: -14 + 14 + 15b + b2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 15b + b2 = 0 + 14 15b + b2 = 0 + 14 Combine like terms: 0 + 14 = 14 15b + b2 = 14 The b term is 15b. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15b + 56.25 + b2 = 14 + 56.25 Reorder the terms: 56.25 + 15b + b2 = 14 + 56.25 Combine like terms: 14 + 56.25 = 70.25 56.25 + 15b + b2 = 70.25 Factor a perfect square on the left side: (b + 7.5)(b + 7.5) = 70.25 Calculate the square root of the right side: 8.381527307 Break this problem into two subproblems by setting (b + 7.5) equal to 8.381527307 and -8.381527307.Subproblem 1
b + 7.5 = 8.381527307 Simplifying b + 7.5 = 8.381527307 Reorder the terms: 7.5 + b = 8.381527307 Solving 7.5 + b = 8.381527307 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + b = 8.381527307 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + b = 8.381527307 + -7.5 b = 8.381527307 + -7.5 Combine like terms: 8.381527307 + -7.5 = 0.881527307 b = 0.881527307 Simplifying b = 0.881527307Subproblem 2
b + 7.5 = -8.381527307 Simplifying b + 7.5 = -8.381527307 Reorder the terms: 7.5 + b = -8.381527307 Solving 7.5 + b = -8.381527307 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + b = -8.381527307 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + b = -8.381527307 + -7.5 b = -8.381527307 + -7.5 Combine like terms: -8.381527307 + -7.5 = -15.881527307 b = -15.881527307 Simplifying b = -15.881527307Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.881527307, -15.881527307}
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