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Simplifying b2 + 11 = 11b Reorder the terms: 11 + b2 = 11b Solving 11 + b2 = 11b Solving for variable 'b'. Reorder the terms: 11 + -11b + b2 = 11b + -11b Combine like terms: 11b + -11b = 0 11 + -11b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + -11b + -11 + b2 = 0 + -11 Reorder the terms: 11 + -11 + -11b + b2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -11b + b2 = 0 + -11 -11b + b2 = 0 + -11 Combine like terms: 0 + -11 = -11 -11b + b2 = -11 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 = -11 + 30.25 Reorder the terms: 30.25 + -11b + b2 = -11 + 30.25 Combine like terms: -11 + 30.25 = 19.25 30.25 + -11b + b2 = 19.25 Factor a perfect square on the left side: (b + -5.5)(b + -5.5) = 19.25 Calculate the square root of the right side: 4.387482194 Break this problem into two subproblems by setting (b + -5.5) equal to 4.387482194 and -4.387482194.Subproblem 1
b + -5.5 = 4.387482194 Simplifying b + -5.5 = 4.387482194 Reorder the terms: -5.5 + b = 4.387482194 Solving -5.5 + b = 4.387482194 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 = 4.387482194 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + b = 4.387482194 + 5.5 b = 4.387482194 + 5.5 Combine like terms: 4.387482194 + 5.5 = 9.887482194 b = 9.887482194 Simplifying b = 9.887482194Subproblem 2
b + -5.5 = -4.387482194 Simplifying b + -5.5 = -4.387482194 Reorder the terms: -5.5 + b = -4.387482194 Solving -5.5 + b = -4.387482194 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 = -4.387482194 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + b = -4.387482194 + 5.5 b = -4.387482194 + 5.5 Combine like terms: -4.387482194 + 5.5 = 1.112517806 b = 1.112517806 Simplifying b = 1.112517806Solution
The solution to the problem is based on the solutions from the subproblems. b = {9.887482194, 1.112517806}
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