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Simplifying b2 + -13b + 27 = 0 Reorder the terms: 27 + -13b + b2 = 0 Solving 27 + -13b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '-27' to each side of the equation. 27 + -13b + -27 + b2 = 0 + -27 Reorder the terms: 27 + -27 + -13b + b2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -13b + b2 = 0 + -27 -13b + b2 = 0 + -27 Combine like terms: 0 + -27 = -27 -13b + b2 = -27 The b term is -13b. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13b + 42.25 + b2 = -27 + 42.25 Reorder the terms: 42.25 + -13b + b2 = -27 + 42.25 Combine like terms: -27 + 42.25 = 15.25 42.25 + -13b + b2 = 15.25 Factor a perfect square on the left side: (b + -6.5)(b + -6.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (b + -6.5) equal to 3.905124838 and -3.905124838.Subproblem 1
b + -6.5 = 3.905124838 Simplifying b + -6.5 = 3.905124838 Reorder the terms: -6.5 + b = 3.905124838 Solving -6.5 + b = 3.905124838 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + b = 3.905124838 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + b = 3.905124838 + 6.5 b = 3.905124838 + 6.5 Combine like terms: 3.905124838 + 6.5 = 10.405124838 b = 10.405124838 Simplifying b = 10.405124838Subproblem 2
b + -6.5 = -3.905124838 Simplifying b + -6.5 = -3.905124838 Reorder the terms: -6.5 + b = -3.905124838 Solving -6.5 + b = -3.905124838 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + b = -3.905124838 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + b = -3.905124838 + 6.5 b = -3.905124838 + 6.5 Combine like terms: -3.905124838 + 6.5 = 2.594875162 b = 2.594875162 Simplifying b = 2.594875162Solution
The solution to the problem is based on the solutions from the subproblems. b = {10.405124838, 2.594875162}
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