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Simplifying b2 + 12b = 21 Reorder the terms: 12b + b2 = 21 Solving 12b + b2 = 21 Solving for variable 'b'. Reorder the terms: -21 + 12b + b2 = 21 + -21 Combine like terms: 21 + -21 = 0 -21 + 12b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + 12b + 21 + b2 = 0 + 21 Reorder the terms: -21 + 21 + 12b + b2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 12b + b2 = 0 + 21 12b + b2 = 0 + 21 Combine like terms: 0 + 21 = 21 12b + b2 = 21 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 = 21 + 36 Reorder the terms: 36 + 12b + b2 = 21 + 36 Combine like terms: 21 + 36 = 57 36 + 12b + b2 = 57 Factor a perfect square on the left side: (b + 6)(b + 6) = 57 Calculate the square root of the right side: 7.549834435 Break this problem into two subproblems by setting (b + 6) equal to 7.549834435 and -7.549834435.Subproblem 1
b + 6 = 7.549834435 Simplifying b + 6 = 7.549834435 Reorder the terms: 6 + b = 7.549834435 Solving 6 + b = 7.549834435 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 = 7.549834435 + -6 Combine like terms: 6 + -6 = 0 0 + b = 7.549834435 + -6 b = 7.549834435 + -6 Combine like terms: 7.549834435 + -6 = 1.549834435 b = 1.549834435 Simplifying b = 1.549834435Subproblem 2
b + 6 = -7.549834435 Simplifying b + 6 = -7.549834435 Reorder the terms: 6 + b = -7.549834435 Solving 6 + b = -7.549834435 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 = -7.549834435 + -6 Combine like terms: 6 + -6 = 0 0 + b = -7.549834435 + -6 b = -7.549834435 + -6 Combine like terms: -7.549834435 + -6 = -13.549834435 b = -13.549834435 Simplifying b = -13.549834435Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.549834435, -13.549834435}
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