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Simplifying k2 + 12k + -41 = 0 Reorder the terms: -41 + 12k + k2 = 0 Solving -41 + 12k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + 12k + 41 + k2 = 0 + 41 Reorder the terms: -41 + 41 + 12k + k2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + 12k + k2 = 0 + 41 12k + k2 = 0 + 41 Combine like terms: 0 + 41 = 41 12k + k2 = 41 The k term is 12k. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12k + 36 + k2 = 41 + 36 Reorder the terms: 36 + 12k + k2 = 41 + 36 Combine like terms: 41 + 36 = 77 36 + 12k + k2 = 77 Factor a perfect square on the left side: (k + 6)(k + 6) = 77 Calculate the square root of the right side: 8.774964387 Break this problem into two subproblems by setting (k + 6) equal to 8.774964387 and -8.774964387.Subproblem 1
k + 6 = 8.774964387 Simplifying k + 6 = 8.774964387 Reorder the terms: 6 + k = 8.774964387 Solving 6 + k = 8.774964387 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + k = 8.774964387 + -6 Combine like terms: 6 + -6 = 0 0 + k = 8.774964387 + -6 k = 8.774964387 + -6 Combine like terms: 8.774964387 + -6 = 2.774964387 k = 2.774964387 Simplifying k = 2.774964387Subproblem 2
k + 6 = -8.774964387 Simplifying k + 6 = -8.774964387 Reorder the terms: 6 + k = -8.774964387 Solving 6 + k = -8.774964387 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + k = -8.774964387 + -6 Combine like terms: 6 + -6 = 0 0 + k = -8.774964387 + -6 k = -8.774964387 + -6 Combine like terms: -8.774964387 + -6 = -14.774964387 k = -14.774964387 Simplifying k = -14.774964387Solution
The solution to the problem is based on the solutions from the subproblems. k = {2.774964387, -14.774964387}
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