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Simplifying 12b + b2 = -22 Solving 12b + b2 = -22 Solving for variable 'b'. Reorder the terms: 22 + 12b + b2 = -22 + 22 Combine like terms: -22 + 22 = 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 = 14 36 + 12b + b2 = 14 Factor a perfect square on the left side: (b + 6)(b + 6) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (b + 6) equal to 3.741657387 and -3.741657387.Subproblem 1
b + 6 = 3.741657387 Simplifying b + 6 = 3.741657387 Reorder the terms: 6 + b = 3.741657387 Solving 6 + b = 3.741657387 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 = 3.741657387 + -6 Combine like terms: 6 + -6 = 0 0 + b = 3.741657387 + -6 b = 3.741657387 + -6 Combine like terms: 3.741657387 + -6 = -2.258342613 b = -2.258342613 Simplifying b = -2.258342613Subproblem 2
b + 6 = -3.741657387 Simplifying b + 6 = -3.741657387 Reorder the terms: 6 + b = -3.741657387 Solving 6 + b = -3.741657387 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 = -3.741657387 + -6 Combine like terms: 6 + -6 = 0 0 + b = -3.741657387 + -6 b = -3.741657387 + -6 Combine like terms: -3.741657387 + -6 = -9.741657387 b = -9.741657387 Simplifying b = -9.741657387Solution
The solution to the problem is based on the solutions from the subproblems. b = {-2.258342613, -9.741657387}
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