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Simplifying b2 + 9b + -384 = 0 Reorder the terms: -384 + 9b + b2 = 0 Solving -384 + 9b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '384' to each side of the equation. -384 + 9b + 384 + b2 = 0 + 384 Reorder the terms: -384 + 384 + 9b + b2 = 0 + 384 Combine like terms: -384 + 384 = 0 0 + 9b + b2 = 0 + 384 9b + b2 = 0 + 384 Combine like terms: 0 + 384 = 384 9b + b2 = 384 The b term is 9b. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9b + 20.25 + b2 = 384 + 20.25 Reorder the terms: 20.25 + 9b + b2 = 384 + 20.25 Combine like terms: 384 + 20.25 = 404.25 20.25 + 9b + b2 = 404.25 Factor a perfect square on the left side: (b + 4.5)(b + 4.5) = 404.25 Calculate the square root of the right side: 20.105969263 Break this problem into two subproblems by setting (b + 4.5) equal to 20.105969263 and -20.105969263.Subproblem 1
b + 4.5 = 20.105969263 Simplifying b + 4.5 = 20.105969263 Reorder the terms: 4.5 + b = 20.105969263 Solving 4.5 + b = 20.105969263 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + b = 20.105969263 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + b = 20.105969263 + -4.5 b = 20.105969263 + -4.5 Combine like terms: 20.105969263 + -4.5 = 15.605969263 b = 15.605969263 Simplifying b = 15.605969263Subproblem 2
b + 4.5 = -20.105969263 Simplifying b + 4.5 = -20.105969263 Reorder the terms: 4.5 + b = -20.105969263 Solving 4.5 + b = -20.105969263 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + b = -20.105969263 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + b = -20.105969263 + -4.5 b = -20.105969263 + -4.5 Combine like terms: -20.105969263 + -4.5 = -24.605969263 b = -24.605969263 Simplifying b = -24.605969263Solution
The solution to the problem is based on the solutions from the subproblems. b = {15.605969263, -24.605969263}
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