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Simplifying b2 + 10b + 25 = 11 Reorder the terms: 25 + 10b + b2 = 11 Solving 25 + 10b + b2 = 11 Solving for variable 'b'. Reorder the terms: 25 + -11 + 10b + b2 = 11 + -11 Combine like terms: 25 + -11 = 14 14 + 10b + b2 = 11 + -11 Combine like terms: 11 + -11 = 0 14 + 10b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + 10b + -14 + b2 = 0 + -14 Reorder the terms: 14 + -14 + 10b + b2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 10b + b2 = 0 + -14 10b + b2 = 0 + -14 Combine like terms: 0 + -14 = -14 10b + b2 = -14 The b term is 10b. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10b + 25 + b2 = -14 + 25 Reorder the terms: 25 + 10b + b2 = -14 + 25 Combine like terms: -14 + 25 = 11 25 + 10b + b2 = 11 Factor a perfect square on the left side: (b + 5)(b + 5) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (b + 5) equal to 3.31662479 and -3.31662479.Subproblem 1
b + 5 = 3.31662479 Simplifying b + 5 = 3.31662479 Reorder the terms: 5 + b = 3.31662479 Solving 5 + b = 3.31662479 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + b = 3.31662479 + -5 Combine like terms: 5 + -5 = 0 0 + b = 3.31662479 + -5 b = 3.31662479 + -5 Combine like terms: 3.31662479 + -5 = -1.68337521 b = -1.68337521 Simplifying b = -1.68337521Subproblem 2
b + 5 = -3.31662479 Simplifying b + 5 = -3.31662479 Reorder the terms: 5 + b = -3.31662479 Solving 5 + b = -3.31662479 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + b = -3.31662479 + -5 Combine like terms: 5 + -5 = 0 0 + b = -3.31662479 + -5 b = -3.31662479 + -5 Combine like terms: -3.31662479 + -5 = -8.31662479 b = -8.31662479 Simplifying b = -8.31662479Solution
The solution to the problem is based on the solutions from the subproblems. b = {-1.68337521, -8.31662479}
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