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Simplifying b2 + 9b + 20.25 = 0 Reorder the terms: 20.25 + 9b + b2 = 0 Solving 20.25 + 9b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '-20.25' to each side of the equation. 20.25 + 9b + -20.25 + b2 = 0 + -20.25 Reorder the terms: 20.25 + -20.25 + 9b + b2 = 0 + -20.25 Combine like terms: 20.25 + -20.25 = 0.00 0.00 + 9b + b2 = 0 + -20.25 9b + b2 = 0 + -20.25 Combine like terms: 0 + -20.25 = -20.25 9b + b2 = -20.25 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 = -20.25 + 20.25 Reorder the terms: 20.25 + 9b + b2 = -20.25 + 20.25 Combine like terms: -20.25 + 20.25 = 0.00 20.25 + 9b + b2 = 0.00 Factor a perfect square on the left side: (b + 4.5)(b + 4.5) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (b + 4.5) equal to 0.00 and 0.00.Subproblem 1
b + 4.5 = 0.00 Simplifying b + 4.5 = 0.00 Reorder the terms: 4.5 + b = 0.00 Solving 4.5 + b = 0.00 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 = 0.00 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + b = 0.00 + -4.5 b = 0.00 + -4.5 Combine like terms: 0.00 + -4.5 = -4.5 b = -4.5 Simplifying b = -4.5Subproblem 2
b + 4.5 = 0.00 Simplifying b + 4.5 = 0.00 Reorder the terms: 4.5 + b = 0.00 Solving 4.5 + b = 0.00 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 = 0.00 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + b = 0.00 + -4.5 b = 0.00 + -4.5 Combine like terms: 0.00 + -4.5 = -4.5 b = -4.5 Simplifying b = -4.5Solution
The solution to the problem is based on the solutions from the subproblems. b = {-4.5, -4.5}
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