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Simplifying k2 + -18k + 35 = 0 Reorder the terms: 35 + -18k + k2 = 0 Solving 35 + -18k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '-35' to each side of the equation. 35 + -18k + -35 + k2 = 0 + -35 Reorder the terms: 35 + -35 + -18k + k2 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + -18k + k2 = 0 + -35 -18k + k2 = 0 + -35 Combine like terms: 0 + -35 = -35 -18k + k2 = -35 The k term is -18k. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18k + 81 + k2 = -35 + 81 Reorder the terms: 81 + -18k + k2 = -35 + 81 Combine like terms: -35 + 81 = 46 81 + -18k + k2 = 46 Factor a perfect square on the left side: (k + -9)(k + -9) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (k + -9) equal to 6.782329983 and -6.782329983.Subproblem 1
k + -9 = 6.782329983 Simplifying k + -9 = 6.782329983 Reorder the terms: -9 + k = 6.782329983 Solving -9 + k = 6.782329983 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + k = 6.782329983 + 9 Combine like terms: -9 + 9 = 0 0 + k = 6.782329983 + 9 k = 6.782329983 + 9 Combine like terms: 6.782329983 + 9 = 15.782329983 k = 15.782329983 Simplifying k = 15.782329983Subproblem 2
k + -9 = -6.782329983 Simplifying k + -9 = -6.782329983 Reorder the terms: -9 + k = -6.782329983 Solving -9 + k = -6.782329983 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + k = -6.782329983 + 9 Combine like terms: -9 + 9 = 0 0 + k = -6.782329983 + 9 k = -6.782329983 + 9 Combine like terms: -6.782329983 + 9 = 2.217670017 k = 2.217670017 Simplifying k = 2.217670017Solution
The solution to the problem is based on the solutions from the subproblems. k = {15.782329983, 2.217670017}
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