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Simplifying k2 + -10k + 26 = 8 Reorder the terms: 26 + -10k + k2 = 8 Solving 26 + -10k + k2 = 8 Solving for variable 'k'. Reorder the terms: 26 + -8 + -10k + k2 = 8 + -8 Combine like terms: 26 + -8 = 18 18 + -10k + k2 = 8 + -8 Combine like terms: 8 + -8 = 0 18 + -10k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + -10k + -18 + k2 = 0 + -18 Reorder the terms: 18 + -18 + -10k + k2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -10k + k2 = 0 + -18 -10k + k2 = 0 + -18 Combine like terms: 0 + -18 = -18 -10k + k2 = -18 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 = -18 + 25 Reorder the terms: 25 + -10k + k2 = -18 + 25 Combine like terms: -18 + 25 = 7 25 + -10k + k2 = 7 Factor a perfect square on the left side: (k + -5)(k + -5) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (k + -5) equal to 2.645751311 and -2.645751311.Subproblem 1
k + -5 = 2.645751311 Simplifying k + -5 = 2.645751311 Reorder the terms: -5 + k = 2.645751311 Solving -5 + k = 2.645751311 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 = 2.645751311 + 5 Combine like terms: -5 + 5 = 0 0 + k = 2.645751311 + 5 k = 2.645751311 + 5 Combine like terms: 2.645751311 + 5 = 7.645751311 k = 7.645751311 Simplifying k = 7.645751311Subproblem 2
k + -5 = -2.645751311 Simplifying k + -5 = -2.645751311 Reorder the terms: -5 + k = -2.645751311 Solving -5 + k = -2.645751311 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 = -2.645751311 + 5 Combine like terms: -5 + 5 = 0 0 + k = -2.645751311 + 5 k = -2.645751311 + 5 Combine like terms: -2.645751311 + 5 = 2.354248689 k = 2.354248689 Simplifying k = 2.354248689Solution
The solution to the problem is based on the solutions from the subproblems. k = {7.645751311, 2.354248689}
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