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Simplifying 9b2 + -8b + -8 = 0 Reorder the terms: -8 + -8b + 9b2 = 0 Solving -8 + -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'. -0.8888888889 + -0.8888888889b + b2 = 0 Move the constant term to the right: Add '0.8888888889' to each side of the equation. -0.8888888889 + -0.8888888889b + 0.8888888889 + b2 = 0 + 0.8888888889 Reorder the terms: -0.8888888889 + 0.8888888889 + -0.8888888889b + b2 = 0 + 0.8888888889 Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000 0.0000000000 + -0.8888888889b + b2 = 0 + 0.8888888889 -0.8888888889b + b2 = 0 + 0.8888888889 Combine like terms: 0 + 0.8888888889 = 0.8888888889 -0.8888888889b + b2 = 0.8888888889 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 = 0.8888888889 + 0.1975308642 Reorder the terms: 0.1975308642 + -0.8888888889b + b2 = 0.8888888889 + 0.1975308642 Combine like terms: 0.8888888889 + 0.1975308642 = 1.0864197531 0.1975308642 + -0.8888888889b + b2 = 1.0864197531 Factor a perfect square on the left side: (b + -0.4444444445)(b + -0.4444444445) = 1.0864197531 Calculate the square root of the right side: 1.042314613 Break this problem into two subproblems by setting (b + -0.4444444445) equal to 1.042314613 and -1.042314613.Subproblem 1
b + -0.4444444445 = 1.042314613 Simplifying b + -0.4444444445 = 1.042314613 Reorder the terms: -0.4444444445 + b = 1.042314613 Solving -0.4444444445 + b = 1.042314613 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 = 1.042314613 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + b = 1.042314613 + 0.4444444445 b = 1.042314613 + 0.4444444445 Combine like terms: 1.042314613 + 0.4444444445 = 1.4867590575 b = 1.4867590575 Simplifying b = 1.4867590575Subproblem 2
b + -0.4444444445 = -1.042314613 Simplifying b + -0.4444444445 = -1.042314613 Reorder the terms: -0.4444444445 + b = -1.042314613 Solving -0.4444444445 + b = -1.042314613 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 = -1.042314613 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + b = -1.042314613 + 0.4444444445 b = -1.042314613 + 0.4444444445 Combine like terms: -1.042314613 + 0.4444444445 = -0.5978701685 b = -0.5978701685 Simplifying b = -0.5978701685Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.4867590575, -0.5978701685}
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