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Simplifying b2 + -22 = 12b Reorder the terms: -22 + b2 = 12b Solving -22 + b2 = 12b Solving for variable 'b'. Reorder the terms: -22 + -12b + b2 = 12b + -12b Combine like terms: 12b + -12b = 0 -22 + -12b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + -12b + 22 + b2 = 0 + 22 Reorder the terms: -22 + 22 + -12b + b2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + -12b + b2 = 0 + 22 -12b + b2 = 0 + 22 Combine like terms: 0 + 22 = 22 -12b + b2 = 22 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 = 22 + 36 Reorder the terms: 36 + -12b + b2 = 22 + 36 Combine like terms: 22 + 36 = 58 36 + -12b + b2 = 58 Factor a perfect square on the left side: (b + -6)(b + -6) = 58 Calculate the square root of the right side: 7.615773106 Break this problem into two subproblems by setting (b + -6) equal to 7.615773106 and -7.615773106.Subproblem 1
b + -6 = 7.615773106 Simplifying b + -6 = 7.615773106 Reorder the terms: -6 + b = 7.615773106 Solving -6 + b = 7.615773106 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 = 7.615773106 + 6 Combine like terms: -6 + 6 = 0 0 + b = 7.615773106 + 6 b = 7.615773106 + 6 Combine like terms: 7.615773106 + 6 = 13.615773106 b = 13.615773106 Simplifying b = 13.615773106Subproblem 2
b + -6 = -7.615773106 Simplifying b + -6 = -7.615773106 Reorder the terms: -6 + b = -7.615773106 Solving -6 + b = -7.615773106 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 = -7.615773106 + 6 Combine like terms: -6 + 6 = 0 0 + b = -7.615773106 + 6 b = -7.615773106 + 6 Combine like terms: -7.615773106 + 6 = -1.615773106 b = -1.615773106 Simplifying b = -1.615773106Solution
The solution to the problem is based on the solutions from the subproblems. b = {13.615773106, -1.615773106}
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