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Simplifying b2 + -17b + 32 = 0 Reorder the terms: 32 + -17b + b2 = 0 Solving 32 + -17b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '-32' to each side of the equation. 32 + -17b + -32 + b2 = 0 + -32 Reorder the terms: 32 + -32 + -17b + b2 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + -17b + b2 = 0 + -32 -17b + b2 = 0 + -32 Combine like terms: 0 + -32 = -32 -17b + b2 = -32 The b term is -17b. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17b + 72.25 + b2 = -32 + 72.25 Reorder the terms: 72.25 + -17b + b2 = -32 + 72.25 Combine like terms: -32 + 72.25 = 40.25 72.25 + -17b + b2 = 40.25 Factor a perfect square on the left side: (b + -8.5)(b + -8.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (b + -8.5) equal to 6.34428877 and -6.34428877.Subproblem 1
b + -8.5 = 6.34428877 Simplifying b + -8.5 = 6.34428877 Reorder the terms: -8.5 + b = 6.34428877 Solving -8.5 + b = 6.34428877 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + b = 6.34428877 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + b = 6.34428877 + 8.5 b = 6.34428877 + 8.5 Combine like terms: 6.34428877 + 8.5 = 14.84428877 b = 14.84428877 Simplifying b = 14.84428877Subproblem 2
b + -8.5 = -6.34428877 Simplifying b + -8.5 = -6.34428877 Reorder the terms: -8.5 + b = -6.34428877 Solving -8.5 + b = -6.34428877 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + b = -6.34428877 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + b = -6.34428877 + 8.5 b = -6.34428877 + 8.5 Combine like terms: -6.34428877 + 8.5 = 2.15571123 b = 2.15571123 Simplifying b = 2.15571123Solution
The solution to the problem is based on the solutions from the subproblems. b = {14.84428877, 2.15571123}
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