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Simplifying b2 + 11b + 20 = 0 Reorder the terms: 20 + 11b + b2 = 0 Solving 20 + 11b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + 11b + -20 + b2 = 0 + -20 Reorder the terms: 20 + -20 + 11b + b2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 11b + b2 = 0 + -20 11b + b2 = 0 + -20 Combine like terms: 0 + -20 = -20 11b + b2 = -20 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 = -20 + 30.25 Reorder the terms: 30.25 + 11b + b2 = -20 + 30.25 Combine like terms: -20 + 30.25 = 10.25 30.25 + 11b + b2 = 10.25 Factor a perfect square on the left side: (b + 5.5)(b + 5.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (b + 5.5) equal to 3.201562119 and -3.201562119.Subproblem 1
b + 5.5 = 3.201562119 Simplifying b + 5.5 = 3.201562119 Reorder the terms: 5.5 + b = 3.201562119 Solving 5.5 + b = 3.201562119 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 = 3.201562119 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + b = 3.201562119 + -5.5 b = 3.201562119 + -5.5 Combine like terms: 3.201562119 + -5.5 = -2.298437881 b = -2.298437881 Simplifying b = -2.298437881Subproblem 2
b + 5.5 = -3.201562119 Simplifying b + 5.5 = -3.201562119 Reorder the terms: 5.5 + b = -3.201562119 Solving 5.5 + b = -3.201562119 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 = -3.201562119 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + b = -3.201562119 + -5.5 b = -3.201562119 + -5.5 Combine like terms: -3.201562119 + -5.5 = -8.701562119 b = -8.701562119 Simplifying b = -8.701562119Solution
The solution to the problem is based on the solutions from the subproblems. b = {-2.298437881, -8.701562119}
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