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Simplifying b2 + 12b + 21 = 0 Reorder the terms: 21 + 12b + b2 = 0 Solving 21 + 12b + b2 = 0 Solving for variable 'b'. 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 = 15 36 + 12b + b2 = 15 Factor a perfect square on the left side: (b + 6)(b + 6) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (b + 6) equal to 3.872983346 and -3.872983346.Subproblem 1
b + 6 = 3.872983346 Simplifying b + 6 = 3.872983346 Reorder the terms: 6 + b = 3.872983346 Solving 6 + b = 3.872983346 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 = 3.872983346 + -6 Combine like terms: 6 + -6 = 0 0 + b = 3.872983346 + -6 b = 3.872983346 + -6 Combine like terms: 3.872983346 + -6 = -2.127016654 b = -2.127016654 Simplifying b = -2.127016654Subproblem 2
b + 6 = -3.872983346 Simplifying b + 6 = -3.872983346 Reorder the terms: 6 + b = -3.872983346 Solving 6 + b = -3.872983346 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 = -3.872983346 + -6 Combine like terms: 6 + -6 = 0 0 + b = -3.872983346 + -6 b = -3.872983346 + -6 Combine like terms: -3.872983346 + -6 = -9.872983346 b = -9.872983346 Simplifying b = -9.872983346Solution
The solution to the problem is based on the solutions from the subproblems. b = {-2.127016654, -9.872983346}
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