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Simplifying 9b2 + 8b + -5 = 0 Reorder the terms: -5 + 8b + 9b2 = 0 Solving -5 + 8b + 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'. -0.5555555556 + 0.8888888889b + b2 = 0 Move the constant term to the right: Add '0.5555555556' to each side of the equation. -0.5555555556 + 0.8888888889b + 0.5555555556 + b2 = 0 + 0.5555555556 Reorder the terms: -0.5555555556 + 0.5555555556 + 0.8888888889b + b2 = 0 + 0.5555555556 Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000 0.0000000000 + 0.8888888889b + b2 = 0 + 0.5555555556 0.8888888889b + b2 = 0 + 0.5555555556 Combine like terms: 0 + 0.5555555556 = 0.5555555556 0.8888888889b + b2 = 0.5555555556 The b term is 0.8888888889b. Take half its coefficient (0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. 0.8888888889b + 0.1975308642 + b2 = 0.5555555556 + 0.1975308642 Reorder the terms: 0.1975308642 + 0.8888888889b + b2 = 0.5555555556 + 0.1975308642 Combine like terms: 0.5555555556 + 0.1975308642 = 0.7530864198 0.1975308642 + 0.8888888889b + b2 = 0.7530864198 Factor a perfect square on the left side: (b + 0.4444444445)(b + 0.4444444445) = 0.7530864198 Calculate the square root of the right side: 0.86780552 Break this problem into two subproblems by setting (b + 0.4444444445) equal to 0.86780552 and -0.86780552.Subproblem 1
b + 0.4444444445 = 0.86780552 Simplifying b + 0.4444444445 = 0.86780552 Reorder the terms: 0.4444444445 + b = 0.86780552 Solving 0.4444444445 + b = 0.86780552 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + b = 0.86780552 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + b = 0.86780552 + -0.4444444445 b = 0.86780552 + -0.4444444445 Combine like terms: 0.86780552 + -0.4444444445 = 0.4233610755 b = 0.4233610755 Simplifying b = 0.4233610755Subproblem 2
b + 0.4444444445 = -0.86780552 Simplifying b + 0.4444444445 = -0.86780552 Reorder the terms: 0.4444444445 + b = -0.86780552 Solving 0.4444444445 + b = -0.86780552 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + b = -0.86780552 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + b = -0.86780552 + -0.4444444445 b = -0.86780552 + -0.4444444445 Combine like terms: -0.86780552 + -0.4444444445 = -1.3122499645 b = -1.3122499645 Simplifying b = -1.3122499645Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.4233610755, -1.3122499645}
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