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Simplifying k2 + -10k + -27 = -6 Reorder the terms: -27 + -10k + k2 = -6 Solving -27 + -10k + k2 = -6 Solving for variable 'k'. Reorder the terms: -27 + 6 + -10k + k2 = -6 + 6 Combine like terms: -27 + 6 = -21 -21 + -10k + k2 = -6 + 6 Combine like terms: -6 + 6 = 0 -21 + -10k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + -10k + 21 + k2 = 0 + 21 Reorder the terms: -21 + 21 + -10k + k2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -10k + k2 = 0 + 21 -10k + k2 = 0 + 21 Combine like terms: 0 + 21 = 21 -10k + k2 = 21 The k term is -10k. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10k + 25 + k2 = 21 + 25 Reorder the terms: 25 + -10k + k2 = 21 + 25 Combine like terms: 21 + 25 = 46 25 + -10k + k2 = 46 Factor a perfect square on the left side: (k + -5)(k + -5) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (k + -5) equal to 6.782329983 and -6.782329983.Subproblem 1
k + -5 = 6.782329983 Simplifying k + -5 = 6.782329983 Reorder the terms: -5 + k = 6.782329983 Solving -5 + k = 6.782329983 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + k = 6.782329983 + 5 Combine like terms: -5 + 5 = 0 0 + k = 6.782329983 + 5 k = 6.782329983 + 5 Combine like terms: 6.782329983 + 5 = 11.782329983 k = 11.782329983 Simplifying k = 11.782329983Subproblem 2
k + -5 = -6.782329983 Simplifying k + -5 = -6.782329983 Reorder the terms: -5 + k = -6.782329983 Solving -5 + k = -6.782329983 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + k = -6.782329983 + 5 Combine like terms: -5 + 5 = 0 0 + k = -6.782329983 + 5 k = -6.782329983 + 5 Combine like terms: -6.782329983 + 5 = -1.782329983 k = -1.782329983 Simplifying k = -1.782329983Solution
The solution to the problem is based on the solutions from the subproblems. k = {11.782329983, -1.782329983}
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