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Simplifying k2 + -12k = -29 Reorder the terms: -12k + k2 = -29 Solving -12k + k2 = -29 Solving for variable 'k'. Reorder the terms: 29 + -12k + k2 = -29 + 29 Combine like terms: -29 + 29 = 0 29 + -12k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '-29' to each side of the equation. 29 + -12k + -29 + k2 = 0 + -29 Reorder the terms: 29 + -29 + -12k + k2 = 0 + -29 Combine like terms: 29 + -29 = 0 0 + -12k + k2 = 0 + -29 -12k + k2 = 0 + -29 Combine like terms: 0 + -29 = -29 -12k + k2 = -29 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 = -29 + 36 Reorder the terms: 36 + -12k + k2 = -29 + 36 Combine like terms: -29 + 36 = 7 36 + -12k + k2 = 7 Factor a perfect square on the left side: (k + -6)(k + -6) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (k + -6) equal to 2.645751311 and -2.645751311.Subproblem 1
k + -6 = 2.645751311 Simplifying k + -6 = 2.645751311 Reorder the terms: -6 + k = 2.645751311 Solving -6 + k = 2.645751311 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 = 2.645751311 + 6 Combine like terms: -6 + 6 = 0 0 + k = 2.645751311 + 6 k = 2.645751311 + 6 Combine like terms: 2.645751311 + 6 = 8.645751311 k = 8.645751311 Simplifying k = 8.645751311Subproblem 2
k + -6 = -2.645751311 Simplifying k + -6 = -2.645751311 Reorder the terms: -6 + k = -2.645751311 Solving -6 + k = -2.645751311 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 = -2.645751311 + 6 Combine like terms: -6 + 6 = 0 0 + k = -2.645751311 + 6 k = -2.645751311 + 6 Combine like terms: -2.645751311 + 6 = 3.354248689 k = 3.354248689 Simplifying k = 3.354248689Solution
The solution to the problem is based on the solutions from the subproblems. k = {8.645751311, 3.354248689}
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