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Simplifying 9b2 + -12b = 4 Reorder the terms: -12b + 9b2 = 4 Solving -12b + 9b2 = 4 Solving for variable 'b'. Reorder the terms: -4 + -12b + 9b2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + -12b + 9b2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.4444444444 + -1.333333333b + b2 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + -1.333333333b + 0.4444444444 + b2 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + -1.333333333b + b2 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + -1.333333333b + b2 = 0 + 0.4444444444 -1.333333333b + b2 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 -1.333333333b + b2 = 0.4444444444 The b term is -1.333333333b. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333b + 0.4444444442 + b2 = 0.4444444444 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333b + b2 = 0.4444444444 + 0.4444444442 Combine like terms: 0.4444444444 + 0.4444444442 = 0.8888888886 0.4444444442 + -1.333333333b + b2 = 0.8888888886 Factor a perfect square on the left side: (b + -0.6666666665)(b + -0.6666666665) = 0.8888888886 Calculate the square root of the right side: 0.942809041 Break this problem into two subproblems by setting (b + -0.6666666665) equal to 0.942809041 and -0.942809041.Subproblem 1
b + -0.6666666665 = 0.942809041 Simplifying b + -0.6666666665 = 0.942809041 Reorder the terms: -0.6666666665 + b = 0.942809041 Solving -0.6666666665 + b = 0.942809041 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + b = 0.942809041 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + b = 0.942809041 + 0.6666666665 b = 0.942809041 + 0.6666666665 Combine like terms: 0.942809041 + 0.6666666665 = 1.6094757075 b = 1.6094757075 Simplifying b = 1.6094757075Subproblem 2
b + -0.6666666665 = -0.942809041 Simplifying b + -0.6666666665 = -0.942809041 Reorder the terms: -0.6666666665 + b = -0.942809041 Solving -0.6666666665 + b = -0.942809041 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + b = -0.942809041 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + b = -0.942809041 + 0.6666666665 b = -0.942809041 + 0.6666666665 Combine like terms: -0.942809041 + 0.6666666665 = -0.2761423745 b = -0.2761423745 Simplifying b = -0.2761423745Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.6094757075, -0.2761423745}
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