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Simplifying b * b + b = 15 Multiply b * b b2 + b = 15 Reorder the terms: b + b2 = 15 Solving b + b2 = 15 Solving for variable 'b'. Reorder the terms: -15 + b + b2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + b + 15 + b2 = 0 + 15 Reorder the terms: -15 + 15 + b + b2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + b + b2 = 0 + 15 b + b2 = 0 + 15 Combine like terms: 0 + 15 = 15 b + b2 = 15 The b term is b. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. b + 0.25 + b2 = 15 + 0.25 Reorder the terms: 0.25 + b + b2 = 15 + 0.25 Combine like terms: 15 + 0.25 = 15.25 0.25 + b + b2 = 15.25 Factor a perfect square on the left side: (b + 0.5)(b + 0.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (b + 0.5) equal to 3.905124838 and -3.905124838.Subproblem 1
b + 0.5 = 3.905124838 Simplifying b + 0.5 = 3.905124838 Reorder the terms: 0.5 + b = 3.905124838 Solving 0.5 + b = 3.905124838 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + b = 3.905124838 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = 3.905124838 + -0.5 b = 3.905124838 + -0.5 Combine like terms: 3.905124838 + -0.5 = 3.405124838 b = 3.405124838 Simplifying b = 3.405124838Subproblem 2
b + 0.5 = -3.905124838 Simplifying b + 0.5 = -3.905124838 Reorder the terms: 0.5 + b = -3.905124838 Solving 0.5 + b = -3.905124838 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + b = -3.905124838 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = -3.905124838 + -0.5 b = -3.905124838 + -0.5 Combine like terms: -3.905124838 + -0.5 = -4.405124838 b = -4.405124838 Simplifying b = -4.405124838Solution
The solution to the problem is based on the solutions from the subproblems. b = {3.405124838, -4.405124838}
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