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Simplifying k2 + -6k + -29 = 0 Reorder the terms: -29 + -6k + k2 = 0 Solving -29 + -6k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + -6k + 29 + k2 = 0 + 29 Reorder the terms: -29 + 29 + -6k + k2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + -6k + k2 = 0 + 29 -6k + k2 = 0 + 29 Combine like terms: 0 + 29 = 29 -6k + k2 = 29 The k term is -6k. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6k + 9 + k2 = 29 + 9 Reorder the terms: 9 + -6k + k2 = 29 + 9 Combine like terms: 29 + 9 = 38 9 + -6k + k2 = 38 Factor a perfect square on the left side: (k + -3)(k + -3) = 38 Calculate the square root of the right side: 6.164414003 Break this problem into two subproblems by setting (k + -3) equal to 6.164414003 and -6.164414003.Subproblem 1
k + -3 = 6.164414003 Simplifying k + -3 = 6.164414003 Reorder the terms: -3 + k = 6.164414003 Solving -3 + k = 6.164414003 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + k = 6.164414003 + 3 Combine like terms: -3 + 3 = 0 0 + k = 6.164414003 + 3 k = 6.164414003 + 3 Combine like terms: 6.164414003 + 3 = 9.164414003 k = 9.164414003 Simplifying k = 9.164414003Subproblem 2
k + -3 = -6.164414003 Simplifying k + -3 = -6.164414003 Reorder the terms: -3 + k = -6.164414003 Solving -3 + k = -6.164414003 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + k = -6.164414003 + 3 Combine like terms: -3 + 3 = 0 0 + k = -6.164414003 + 3 k = -6.164414003 + 3 Combine like terms: -6.164414003 + 3 = -3.164414003 k = -3.164414003 Simplifying k = -3.164414003Solution
The solution to the problem is based on the solutions from the subproblems. k = {9.164414003, -3.164414003}
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