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Simplifying b2 + 16 = -9b Reorder the terms: 16 + b2 = -9b Solving 16 + b2 = -9b Solving for variable 'b'. Reorder the terms: 16 + 9b + b2 = -9b + 9b Combine like terms: -9b + 9b = 0 16 + 9b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + 9b + -16 + b2 = 0 + -16 Reorder the terms: 16 + -16 + 9b + b2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + 9b + b2 = 0 + -16 9b + b2 = 0 + -16 Combine like terms: 0 + -16 = -16 9b + b2 = -16 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 = -16 + 20.25 Reorder the terms: 20.25 + 9b + b2 = -16 + 20.25 Combine like terms: -16 + 20.25 = 4.25 20.25 + 9b + b2 = 4.25 Factor a perfect square on the left side: (b + 4.5)(b + 4.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (b + 4.5) equal to 2.061552813 and -2.061552813.Subproblem 1
b + 4.5 = 2.061552813 Simplifying b + 4.5 = 2.061552813 Reorder the terms: 4.5 + b = 2.061552813 Solving 4.5 + b = 2.061552813 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 = 2.061552813 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + b = 2.061552813 + -4.5 b = 2.061552813 + -4.5 Combine like terms: 2.061552813 + -4.5 = -2.438447187 b = -2.438447187 Simplifying b = -2.438447187Subproblem 2
b + 4.5 = -2.061552813 Simplifying b + 4.5 = -2.061552813 Reorder the terms: 4.5 + b = -2.061552813 Solving 4.5 + b = -2.061552813 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 = -2.061552813 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + b = -2.061552813 + -4.5 b = -2.061552813 + -4.5 Combine like terms: -2.061552813 + -4.5 = -6.561552813 b = -6.561552813 Simplifying b = -6.561552813Solution
The solution to the problem is based on the solutions from the subproblems. b = {-2.438447187, -6.561552813}
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