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Simplifying b2 + -18b = -9 Reorder the terms: -18b + b2 = -9 Solving -18b + b2 = -9 Solving for variable 'b'. Reorder the terms: 9 + -18b + b2 = -9 + 9 Combine like terms: -9 + 9 = 0 9 + -18b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -18b + -9 + b2 = 0 + -9 Reorder the terms: 9 + -9 + -18b + b2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -18b + b2 = 0 + -9 -18b + b2 = 0 + -9 Combine like terms: 0 + -9 = -9 -18b + b2 = -9 The b term is -18b. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18b + 81 + b2 = -9 + 81 Reorder the terms: 81 + -18b + b2 = -9 + 81 Combine like terms: -9 + 81 = 72 81 + -18b + b2 = 72 Factor a perfect square on the left side: (b + -9)(b + -9) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (b + -9) equal to 8.485281374 and -8.485281374.Subproblem 1
b + -9 = 8.485281374 Simplifying b + -9 = 8.485281374 Reorder the terms: -9 + b = 8.485281374 Solving -9 + b = 8.485281374 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + b = 8.485281374 + 9 Combine like terms: -9 + 9 = 0 0 + b = 8.485281374 + 9 b = 8.485281374 + 9 Combine like terms: 8.485281374 + 9 = 17.485281374 b = 17.485281374 Simplifying b = 17.485281374Subproblem 2
b + -9 = -8.485281374 Simplifying b + -9 = -8.485281374 Reorder the terms: -9 + b = -8.485281374 Solving -9 + b = -8.485281374 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + b = -8.485281374 + 9 Combine like terms: -9 + 9 = 0 0 + b = -8.485281374 + 9 b = -8.485281374 + 9 Combine like terms: -8.485281374 + 9 = 0.514718626 b = 0.514718626 Simplifying b = 0.514718626Solution
The solution to the problem is based on the solutions from the subproblems. b = {17.485281374, 0.514718626}
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