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Simplifying 9b2 + -10b + 2 = 0 Reorder the terms: 2 + -10b + 9b2 = 0 Solving 2 + -10b + 9b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.2222222222 + -1.111111111b + b2 = 0 Move the constant term to the right: Add '-0.2222222222' to each side of the equation. 0.2222222222 + -1.111111111b + -0.2222222222 + b2 = 0 + -0.2222222222 Reorder the terms: 0.2222222222 + -0.2222222222 + -1.111111111b + b2 = 0 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + -1.111111111b + b2 = 0 + -0.2222222222 -1.111111111b + b2 = 0 + -0.2222222222 Combine like terms: 0 + -0.2222222222 = -0.2222222222 -1.111111111b + b2 = -0.2222222222 The b term is -1.111111111b. Take half its coefficient (-0.5555555555). Square it (0.3086419752) and add it to both sides. Add '0.3086419752' to each side of the equation. -1.111111111b + 0.3086419752 + b2 = -0.2222222222 + 0.3086419752 Reorder the terms: 0.3086419752 + -1.111111111b + b2 = -0.2222222222 + 0.3086419752 Combine like terms: -0.2222222222 + 0.3086419752 = 0.086419753 0.3086419752 + -1.111111111b + b2 = 0.086419753 Factor a perfect square on the left side: (b + -0.5555555555)(b + -0.5555555555) = 0.086419753 Calculate the square root of the right side: 0.293972368 Break this problem into two subproblems by setting (b + -0.5555555555) equal to 0.293972368 and -0.293972368.Subproblem 1
b + -0.5555555555 = 0.293972368 Simplifying b + -0.5555555555 = 0.293972368 Reorder the terms: -0.5555555555 + b = 0.293972368 Solving -0.5555555555 + b = 0.293972368 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.5555555555' to each side of the equation. -0.5555555555 + 0.5555555555 + b = 0.293972368 + 0.5555555555 Combine like terms: -0.5555555555 + 0.5555555555 = 0.0000000000 0.0000000000 + b = 0.293972368 + 0.5555555555 b = 0.293972368 + 0.5555555555 Combine like terms: 0.293972368 + 0.5555555555 = 0.8495279235 b = 0.8495279235 Simplifying b = 0.8495279235Subproblem 2
b + -0.5555555555 = -0.293972368 Simplifying b + -0.5555555555 = -0.293972368 Reorder the terms: -0.5555555555 + b = -0.293972368 Solving -0.5555555555 + b = -0.293972368 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.5555555555' to each side of the equation. -0.5555555555 + 0.5555555555 + b = -0.293972368 + 0.5555555555 Combine like terms: -0.5555555555 + 0.5555555555 = 0.0000000000 0.0000000000 + b = -0.293972368 + 0.5555555555 b = -0.293972368 + 0.5555555555 Combine like terms: -0.293972368 + 0.5555555555 = 0.2615831875 b = 0.2615831875 Simplifying b = 0.2615831875Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.8495279235, 0.2615831875}
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