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Simplifying b2 + 5 = 8b + 0 Reorder the terms: 5 + b2 = 8b + 0 Reorder the terms: 5 + b2 = 0 + 8b Remove the zero: 5 + b2 = 8b Solving 5 + b2 = 8b Solving for variable 'b'. Reorder the terms: 5 + -8b + b2 = 8b + -8b Combine like terms: 8b + -8b = 0 5 + -8b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -8b + -5 + b2 = 0 + -5 Reorder the terms: 5 + -5 + -8b + b2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -8b + b2 = 0 + -5 -8b + b2 = 0 + -5 Combine like terms: 0 + -5 = -5 -8b + b2 = -5 The b term is -8b. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8b + 16 + b2 = -5 + 16 Reorder the terms: 16 + -8b + b2 = -5 + 16 Combine like terms: -5 + 16 = 11 16 + -8b + b2 = 11 Factor a perfect square on the left side: (b + -4)(b + -4) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (b + -4) equal to 3.31662479 and -3.31662479.Subproblem 1
b + -4 = 3.31662479 Simplifying b + -4 = 3.31662479 Reorder the terms: -4 + b = 3.31662479 Solving -4 + b = 3.31662479 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + b = 3.31662479 + 4 Combine like terms: -4 + 4 = 0 0 + b = 3.31662479 + 4 b = 3.31662479 + 4 Combine like terms: 3.31662479 + 4 = 7.31662479 b = 7.31662479 Simplifying b = 7.31662479Subproblem 2
b + -4 = -3.31662479 Simplifying b + -4 = -3.31662479 Reorder the terms: -4 + b = -3.31662479 Solving -4 + b = -3.31662479 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + b = -3.31662479 + 4 Combine like terms: -4 + 4 = 0 0 + b = -3.31662479 + 4 b = -3.31662479 + 4 Combine like terms: -3.31662479 + 4 = 0.68337521 b = 0.68337521 Simplifying b = 0.68337521Solution
The solution to the problem is based on the solutions from the subproblems. b = {7.31662479, 0.68337521}
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