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Simplifying 11b2 + -47b + -24 = 0 Reorder the terms: -24 + -47b + 11b2 = 0 Solving -24 + -47b + 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 + -4.272727273b + b2 = 0 Move the constant term to the right: Add '2.181818182' to each side of the equation. -2.181818182 + -4.272727273b + 2.181818182 + b2 = 0 + 2.181818182 Reorder the terms: -2.181818182 + 2.181818182 + -4.272727273b + b2 = 0 + 2.181818182 Combine like terms: -2.181818182 + 2.181818182 = 0.000000000 0.000000000 + -4.272727273b + b2 = 0 + 2.181818182 -4.272727273b + b2 = 0 + 2.181818182 Combine like terms: 0 + 2.181818182 = 2.181818182 -4.272727273b + b2 = 2.181818182 The b term is -4.272727273b. Take half its coefficient (-2.136363637). Square it (4.564049590) and add it to both sides. Add '4.564049590' to each side of the equation. -4.272727273b + 4.564049590 + b2 = 2.181818182 + 4.564049590 Reorder the terms: 4.564049590 + -4.272727273b + b2 = 2.181818182 + 4.564049590 Combine like terms: 2.181818182 + 4.564049590 = 6.745867772 4.564049590 + -4.272727273b + b2 = 6.745867772 Factor a perfect square on the left side: (b + -2.136363637)(b + -2.136363637) = 6.745867772 Calculate the square root of the right side: 2.597280842 Break this problem into two subproblems by setting (b + -2.136363637) equal to 2.597280842 and -2.597280842.Subproblem 1
b + -2.136363637 = 2.597280842 Simplifying b + -2.136363637 = 2.597280842 Reorder the terms: -2.136363637 + b = 2.597280842 Solving -2.136363637 + b = 2.597280842 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2.136363637' to each side of the equation. -2.136363637 + 2.136363637 + b = 2.597280842 + 2.136363637 Combine like terms: -2.136363637 + 2.136363637 = 0.000000000 0.000000000 + b = 2.597280842 + 2.136363637 b = 2.597280842 + 2.136363637 Combine like terms: 2.597280842 + 2.136363637 = 4.733644479 b = 4.733644479 Simplifying b = 4.733644479Subproblem 2
b + -2.136363637 = -2.597280842 Simplifying b + -2.136363637 = -2.597280842 Reorder the terms: -2.136363637 + b = -2.597280842 Solving -2.136363637 + b = -2.597280842 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2.136363637' to each side of the equation. -2.136363637 + 2.136363637 + b = -2.597280842 + 2.136363637 Combine like terms: -2.136363637 + 2.136363637 = 0.000000000 0.000000000 + b = -2.597280842 + 2.136363637 b = -2.597280842 + 2.136363637 Combine like terms: -2.597280842 + 2.136363637 = -0.460917205 b = -0.460917205 Simplifying b = -0.460917205Solution
The solution to the problem is based on the solutions from the subproblems. b = {4.733644479, -0.460917205}
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