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Simplifying b2 + -11b = 23 Reorder the terms: -11b + b2 = 23 Solving -11b + b2 = 23 Solving for variable 'b'. Reorder the terms: -23 + -11b + b2 = 23 + -23 Combine like terms: 23 + -23 = 0 -23 + -11b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + -11b + 23 + b2 = 0 + 23 Reorder the terms: -23 + 23 + -11b + b2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -11b + b2 = 0 + 23 -11b + b2 = 0 + 23 Combine like terms: 0 + 23 = 23 -11b + b2 = 23 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 = 23 + 30.25 Reorder the terms: 30.25 + -11b + b2 = 23 + 30.25 Combine like terms: 23 + 30.25 = 53.25 30.25 + -11b + b2 = 53.25 Factor a perfect square on the left side: (b + -5.5)(b + -5.5) = 53.25 Calculate the square root of the right side: 7.29725976 Break this problem into two subproblems by setting (b + -5.5) equal to 7.29725976 and -7.29725976.Subproblem 1
b + -5.5 = 7.29725976 Simplifying b + -5.5 = 7.29725976 Reorder the terms: -5.5 + b = 7.29725976 Solving -5.5 + b = 7.29725976 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 = 7.29725976 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + b = 7.29725976 + 5.5 b = 7.29725976 + 5.5 Combine like terms: 7.29725976 + 5.5 = 12.79725976 b = 12.79725976 Simplifying b = 12.79725976Subproblem 2
b + -5.5 = -7.29725976 Simplifying b + -5.5 = -7.29725976 Reorder the terms: -5.5 + b = -7.29725976 Solving -5.5 + b = -7.29725976 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 = -7.29725976 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + b = -7.29725976 + 5.5 b = -7.29725976 + 5.5 Combine like terms: -7.29725976 + 5.5 = -1.79725976 b = -1.79725976 Simplifying b = -1.79725976Solution
The solution to the problem is based on the solutions from the subproblems. b = {12.79725976, -1.79725976}
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