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Simplifying 11b2 + -52b + -24 = 0 Reorder the terms: -24 + -52b + 11b2 = 0 Solving -24 + -52b + 11b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -2.181818182 + -4.727272727b + b2 = 0 Move the constant term to the right: Add '2.181818182' to each side of the equation. -2.181818182 + -4.727272727b + 2.181818182 + b2 = 0 + 2.181818182 Reorder the terms: -2.181818182 + 2.181818182 + -4.727272727b + b2 = 0 + 2.181818182 Combine like terms: -2.181818182 + 2.181818182 = 0.000000000 0.000000000 + -4.727272727b + b2 = 0 + 2.181818182 -4.727272727b + b2 = 0 + 2.181818182 Combine like terms: 0 + 2.181818182 = 2.181818182 -4.727272727b + b2 = 2.181818182 The b term is -4.727272727b. Take half its coefficient (-2.363636364). Square it (5.586776861) and add it to both sides. Add '5.586776861' to each side of the equation. -4.727272727b + 5.586776861 + b2 = 2.181818182 + 5.586776861 Reorder the terms: 5.586776861 + -4.727272727b + b2 = 2.181818182 + 5.586776861 Combine like terms: 2.181818182 + 5.586776861 = 7.768595043 5.586776861 + -4.727272727b + b2 = 7.768595043 Factor a perfect square on the left side: (b + -2.363636364)(b + -2.363636364) = 7.768595043 Calculate the square root of the right side: 2.787219949 Break this problem into two subproblems by setting (b + -2.363636364) equal to 2.787219949 and -2.787219949.Subproblem 1
b + -2.363636364 = 2.787219949 Simplifying b + -2.363636364 = 2.787219949 Reorder the terms: -2.363636364 + b = 2.787219949 Solving -2.363636364 + b = 2.787219949 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2.363636364' to each side of the equation. -2.363636364 + 2.363636364 + b = 2.787219949 + 2.363636364 Combine like terms: -2.363636364 + 2.363636364 = 0.000000000 0.000000000 + b = 2.787219949 + 2.363636364 b = 2.787219949 + 2.363636364 Combine like terms: 2.787219949 + 2.363636364 = 5.150856313 b = 5.150856313 Simplifying b = 5.150856313Subproblem 2
b + -2.363636364 = -2.787219949 Simplifying b + -2.363636364 = -2.787219949 Reorder the terms: -2.363636364 + b = -2.787219949 Solving -2.363636364 + b = -2.787219949 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2.363636364' to each side of the equation. -2.363636364 + 2.363636364 + b = -2.787219949 + 2.363636364 Combine like terms: -2.363636364 + 2.363636364 = 0.000000000 0.000000000 + b = -2.787219949 + 2.363636364 b = -2.787219949 + 2.363636364 Combine like terms: -2.787219949 + 2.363636364 = -0.423583585 b = -0.423583585 Simplifying b = -0.423583585Solution
The solution to the problem is based on the solutions from the subproblems. b = {5.150856313, -0.423583585}
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