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Simplifying b2 + -13b + 3 = -3 Reorder the terms: 3 + -13b + b2 = -3 Solving 3 + -13b + b2 = -3 Solving for variable 'b'. Reorder the terms: 3 + 3 + -13b + b2 = -3 + 3 Combine like terms: 3 + 3 = 6 6 + -13b + b2 = -3 + 3 Combine like terms: -3 + 3 = 0 6 + -13b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -13b + -6 + b2 = 0 + -6 Reorder the terms: 6 + -6 + -13b + b2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -13b + b2 = 0 + -6 -13b + b2 = 0 + -6 Combine like terms: 0 + -6 = -6 -13b + b2 = -6 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 = -6 + 42.25 Reorder the terms: 42.25 + -13b + b2 = -6 + 42.25 Combine like terms: -6 + 42.25 = 36.25 42.25 + -13b + b2 = 36.25 Factor a perfect square on the left side: (b + -6.5)(b + -6.5) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (b + -6.5) equal to 6.020797289 and -6.020797289.Subproblem 1
b + -6.5 = 6.020797289 Simplifying b + -6.5 = 6.020797289 Reorder the terms: -6.5 + b = 6.020797289 Solving -6.5 + b = 6.020797289 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 = 6.020797289 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + b = 6.020797289 + 6.5 b = 6.020797289 + 6.5 Combine like terms: 6.020797289 + 6.5 = 12.520797289 b = 12.520797289 Simplifying b = 12.520797289Subproblem 2
b + -6.5 = -6.020797289 Simplifying b + -6.5 = -6.020797289 Reorder the terms: -6.5 + b = -6.020797289 Solving -6.5 + b = -6.020797289 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 = -6.020797289 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + b = -6.020797289 + 6.5 b = -6.020797289 + 6.5 Combine like terms: -6.020797289 + 6.5 = 0.479202711 b = 0.479202711 Simplifying b = 0.479202711Solution
The solution to the problem is based on the solutions from the subproblems. b = {12.520797289, 0.479202711}
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