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Simplifying 9b2 = 18 + -11b Solving 9b2 = 18 + -11b Solving for variable 'b'. Reorder the terms: -18 + 11b + 9b2 = 18 + -11b + -18 + 11b Reorder the terms: -18 + 11b + 9b2 = 18 + -18 + -11b + 11b Combine like terms: 18 + -18 = 0 -18 + 11b + 9b2 = 0 + -11b + 11b -18 + 11b + 9b2 = -11b + 11b Combine like terms: -11b + 11b = 0 -18 + 11b + 9b2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2 + 1.222222222b + b2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 1.222222222b + 2 + b2 = 0 + 2 Reorder the terms: -2 + 2 + 1.222222222b + b2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 1.222222222b + b2 = 0 + 2 1.222222222b + b2 = 0 + 2 Combine like terms: 0 + 2 = 2 1.222222222b + b2 = 2 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 = 2 + 0.3734567900 Reorder the terms: 0.3734567900 + 1.222222222b + b2 = 2 + 0.3734567900 Combine like terms: 2 + 0.3734567900 = 2.37345679 0.3734567900 + 1.222222222b + b2 = 2.37345679 Factor a perfect square on the left side: (b + 0.611111111)(b + 0.611111111) = 2.37345679 Calculate the square root of the right side: 1.540602736 Break this problem into two subproblems by setting (b + 0.611111111) equal to 1.540602736 and -1.540602736.Subproblem 1
b + 0.611111111 = 1.540602736 Simplifying b + 0.611111111 = 1.540602736 Reorder the terms: 0.611111111 + b = 1.540602736 Solving 0.611111111 + b = 1.540602736 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 = 1.540602736 + -0.611111111 Combine like terms: 0.611111111 + -0.611111111 = 0.000000000 0.000000000 + b = 1.540602736 + -0.611111111 b = 1.540602736 + -0.611111111 Combine like terms: 1.540602736 + -0.611111111 = 0.929491625 b = 0.929491625 Simplifying b = 0.929491625Subproblem 2
b + 0.611111111 = -1.540602736 Simplifying b + 0.611111111 = -1.540602736 Reorder the terms: 0.611111111 + b = -1.540602736 Solving 0.611111111 + b = -1.540602736 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 = -1.540602736 + -0.611111111 Combine like terms: 0.611111111 + -0.611111111 = 0.000000000 0.000000000 + b = -1.540602736 + -0.611111111 b = -1.540602736 + -0.611111111 Combine like terms: -1.540602736 + -0.611111111 = -2.151713847 b = -2.151713847 Simplifying b = -2.151713847Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.929491625, -2.151713847}
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