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Simplifying -2b2 + -11b + -2 = -3b2 + -1 Reorder the terms: -2 + -11b + -2b2 = -3b2 + -1 Reorder the terms: -2 + -11b + -2b2 = -1 + -3b2 Solving -2 + -11b + -2b2 = -1 + -3b2 Solving for variable 'b'. Reorder the terms: -2 + 1 + -11b + -2b2 + 3b2 = -1 + -3b2 + 1 + 3b2 Combine like terms: -2 + 1 = -1 -1 + -11b + -2b2 + 3b2 = -1 + -3b2 + 1 + 3b2 Combine like terms: -2b2 + 3b2 = 1b2 -1 + -11b + 1b2 = -1 + -3b2 + 1 + 3b2 Reorder the terms: -1 + -11b + 1b2 = -1 + 1 + -3b2 + 3b2 Combine like terms: -1 + 1 = 0 -1 + -11b + 1b2 = 0 + -3b2 + 3b2 -1 + -11b + 1b2 = -3b2 + 3b2 Combine like terms: -3b2 + 3b2 = 0 -1 + -11b + 1b2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -11b + 1 + b2 = 0 + 1 Reorder the terms: -1 + 1 + -11b + b2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -11b + b2 = 0 + 1 -11b + b2 = 0 + 1 Combine like terms: 0 + 1 = 1 -11b + b2 = 1 The b term is -11b. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11b + 30.25 + b2 = 1 + 30.25 Reorder the terms: 30.25 + -11b + b2 = 1 + 30.25 Combine like terms: 1 + 30.25 = 31.25 30.25 + -11b + b2 = 31.25 Factor a perfect square on the left side: (b + -5.5)(b + -5.5) = 31.25 Calculate the square root of the right side: 5.590169944 Break this problem into two subproblems by setting (b + -5.5) equal to 5.590169944 and -5.590169944.Subproblem 1
b + -5.5 = 5.590169944 Simplifying b + -5.5 = 5.590169944 Reorder the terms: -5.5 + b = 5.590169944 Solving -5.5 + b = 5.590169944 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + b = 5.590169944 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + b = 5.590169944 + 5.5 b = 5.590169944 + 5.5 Combine like terms: 5.590169944 + 5.5 = 11.090169944 b = 11.090169944 Simplifying b = 11.090169944Subproblem 2
b + -5.5 = -5.590169944 Simplifying b + -5.5 = -5.590169944 Reorder the terms: -5.5 + b = -5.590169944 Solving -5.5 + b = -5.590169944 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + b = -5.590169944 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + b = -5.590169944 + 5.5 b = -5.590169944 + 5.5 Combine like terms: -5.590169944 + 5.5 = -0.090169944 b = -0.090169944 Simplifying b = -0.090169944Solution
The solution to the problem is based on the solutions from the subproblems. b = {11.090169944, -0.090169944}
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