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Simplifying -17 + 11b + 9b2 = 0 Solving -17 + 11b + 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'. -1.888888889 + 1.222222222b + b2 = 0 Move the constant term to the right: Add '1.888888889' to each side of the equation. -1.888888889 + 1.222222222b + 1.888888889 + b2 = 0 + 1.888888889 Reorder the terms: -1.888888889 + 1.888888889 + 1.222222222b + b2 = 0 + 1.888888889 Combine like terms: -1.888888889 + 1.888888889 = 0.000000000 0.000000000 + 1.222222222b + b2 = 0 + 1.888888889 1.222222222b + b2 = 0 + 1.888888889 Combine like terms: 0 + 1.888888889 = 1.888888889 1.222222222b + b2 = 1.888888889 The b term is 1.222222222b. Take half its coefficient (0.611111111). Square it (0.3734567900) and add it to both sides. Add '0.3734567900' to each side of the equation. 1.222222222b + 0.3734567900 + b2 = 1.888888889 + 0.3734567900 Reorder the terms: 0.3734567900 + 1.222222222b + b2 = 1.888888889 + 0.3734567900 Combine like terms: 1.888888889 + 0.3734567900 = 2.262345679 0.3734567900 + 1.222222222b + b2 = 2.262345679 Factor a perfect square on the left side: (b + 0.611111111)(b + 0.611111111) = 2.262345679 Calculate the square root of the right side: 1.504109597 Break this problem into two subproblems by setting (b + 0.611111111) equal to 1.504109597 and -1.504109597.Subproblem 1
b + 0.611111111 = 1.504109597 Simplifying b + 0.611111111 = 1.504109597 Reorder the terms: 0.611111111 + b = 1.504109597 Solving 0.611111111 + b = 1.504109597 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.611111111' to each side of the equation. 0.611111111 + -0.611111111 + b = 1.504109597 + -0.611111111 Combine like terms: 0.611111111 + -0.611111111 = 0.000000000 0.000000000 + b = 1.504109597 + -0.611111111 b = 1.504109597 + -0.611111111 Combine like terms: 1.504109597 + -0.611111111 = 0.892998486 b = 0.892998486 Simplifying b = 0.892998486Subproblem 2
b + 0.611111111 = -1.504109597 Simplifying b + 0.611111111 = -1.504109597 Reorder the terms: 0.611111111 + b = -1.504109597 Solving 0.611111111 + b = -1.504109597 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.611111111' to each side of the equation. 0.611111111 + -0.611111111 + b = -1.504109597 + -0.611111111 Combine like terms: 0.611111111 + -0.611111111 = 0.000000000 0.000000000 + b = -1.504109597 + -0.611111111 b = -1.504109597 + -0.611111111 Combine like terms: -1.504109597 + -0.611111111 = -2.115220708 b = -2.115220708 Simplifying b = -2.115220708Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.892998486, -2.115220708}
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