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Simplifying 4(b + -8) + 3b(11 + -1b) + -7 = 0 Reorder the terms: 4(-8 + b) + 3b(11 + -1b) + -7 = 0 (-8 * 4 + b * 4) + 3b(11 + -1b) + -7 = 0 (-32 + 4b) + 3b(11 + -1b) + -7 = 0 -32 + 4b + (11 * 3b + -1b * 3b) + -7 = 0 -32 + 4b + (33b + -3b2) + -7 = 0 Reorder the terms: -32 + -7 + 4b + 33b + -3b2 = 0 Combine like terms: -32 + -7 = -39 -39 + 4b + 33b + -3b2 = 0 Combine like terms: 4b + 33b = 37b -39 + 37b + -3b2 = 0 Solving -39 + 37b + -3b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 13 + -12.33333333b + b2 = 0 Move the constant term to the right: Add '-13' to each side of the equation. 13 + -12.33333333b + -13 + b2 = 0 + -13 Reorder the terms: 13 + -13 + -12.33333333b + b2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -12.33333333b + b2 = 0 + -13 -12.33333333b + b2 = 0 + -13 Combine like terms: 0 + -13 = -13 -12.33333333b + b2 = -13 The b term is -12.33333333b. Take half its coefficient (-6.166666665). Square it (38.02777776) and add it to both sides. Add '38.02777776' to each side of the equation. -12.33333333b + 38.02777776 + b2 = -13 + 38.02777776 Reorder the terms: 38.02777776 + -12.33333333b + b2 = -13 + 38.02777776 Combine like terms: -13 + 38.02777776 = 25.02777776 38.02777776 + -12.33333333b + b2 = 25.02777776 Factor a perfect square on the left side: (b + -6.166666665)(b + -6.166666665) = 25.02777776 Calculate the square root of the right side: 5.002777005 Break this problem into two subproblems by setting (b + -6.166666665) equal to 5.002777005 and -5.002777005.Subproblem 1
b + -6.166666665 = 5.002777005 Simplifying b + -6.166666665 = 5.002777005 Reorder the terms: -6.166666665 + b = 5.002777005 Solving -6.166666665 + b = 5.002777005 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '6.166666665' to each side of the equation. -6.166666665 + 6.166666665 + b = 5.002777005 + 6.166666665 Combine like terms: -6.166666665 + 6.166666665 = 0.000000000 0.000000000 + b = 5.002777005 + 6.166666665 b = 5.002777005 + 6.166666665 Combine like terms: 5.002777005 + 6.166666665 = 11.16944367 b = 11.16944367 Simplifying b = 11.16944367Subproblem 2
b + -6.166666665 = -5.002777005 Simplifying b + -6.166666665 = -5.002777005 Reorder the terms: -6.166666665 + b = -5.002777005 Solving -6.166666665 + b = -5.002777005 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '6.166666665' to each side of the equation. -6.166666665 + 6.166666665 + b = -5.002777005 + 6.166666665 Combine like terms: -6.166666665 + 6.166666665 = 0.000000000 0.000000000 + b = -5.002777005 + 6.166666665 b = -5.002777005 + 6.166666665 Combine like terms: -5.002777005 + 6.166666665 = 1.16388966 b = 1.16388966 Simplifying b = 1.16388966Solution
The solution to the problem is based on the solutions from the subproblems. b = {11.16944367, 1.16388966}
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