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Simplifying b2 + -12b + -12 = 5 Reorder the terms: -12 + -12b + b2 = 5 Solving -12 + -12b + b2 = 5 Solving for variable 'b'. Reorder the terms: -12 + -5 + -12b + b2 = 5 + -5 Combine like terms: -12 + -5 = -17 -17 + -12b + b2 = 5 + -5 Combine like terms: 5 + -5 = 0 -17 + -12b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + -12b + 17 + b2 = 0 + 17 Reorder the terms: -17 + 17 + -12b + b2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -12b + b2 = 0 + 17 -12b + b2 = 0 + 17 Combine like terms: 0 + 17 = 17 -12b + b2 = 17 The b term is -12b. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12b + 36 + b2 = 17 + 36 Reorder the terms: 36 + -12b + b2 = 17 + 36 Combine like terms: 17 + 36 = 53 36 + -12b + b2 = 53 Factor a perfect square on the left side: (b + -6)(b + -6) = 53 Calculate the square root of the right side: 7.280109889 Break this problem into two subproblems by setting (b + -6) equal to 7.280109889 and -7.280109889.Subproblem 1
b + -6 = 7.280109889 Simplifying b + -6 = 7.280109889 Reorder the terms: -6 + b = 7.280109889 Solving -6 + b = 7.280109889 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + b = 7.280109889 + 6 Combine like terms: -6 + 6 = 0 0 + b = 7.280109889 + 6 b = 7.280109889 + 6 Combine like terms: 7.280109889 + 6 = 13.280109889 b = 13.280109889 Simplifying b = 13.280109889Subproblem 2
b + -6 = -7.280109889 Simplifying b + -6 = -7.280109889 Reorder the terms: -6 + b = -7.280109889 Solving -6 + b = -7.280109889 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + b = -7.280109889 + 6 Combine like terms: -6 + 6 = 0 0 + b = -7.280109889 + 6 b = -7.280109889 + 6 Combine like terms: -7.280109889 + 6 = -1.280109889 b = -1.280109889 Simplifying b = -1.280109889Solution
The solution to the problem is based on the solutions from the subproblems. b = {13.280109889, -1.280109889}
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