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Simplifying k2 + -26k + -17 = 0 Reorder the terms: -17 + -26k + k2 = 0 Solving -17 + -26k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + -26k + 17 + k2 = 0 + 17 Reorder the terms: -17 + 17 + -26k + k2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -26k + k2 = 0 + 17 -26k + k2 = 0 + 17 Combine like terms: 0 + 17 = 17 -26k + k2 = 17 The k term is -26k. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26k + 169 + k2 = 17 + 169 Reorder the terms: 169 + -26k + k2 = 17 + 169 Combine like terms: 17 + 169 = 186 169 + -26k + k2 = 186 Factor a perfect square on the left side: (k + -13)(k + -13) = 186 Calculate the square root of the right side: 13.638181697 Break this problem into two subproblems by setting (k + -13) equal to 13.638181697 and -13.638181697.Subproblem 1
k + -13 = 13.638181697 Simplifying k + -13 = 13.638181697 Reorder the terms: -13 + k = 13.638181697 Solving -13 + k = 13.638181697 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + k = 13.638181697 + 13 Combine like terms: -13 + 13 = 0 0 + k = 13.638181697 + 13 k = 13.638181697 + 13 Combine like terms: 13.638181697 + 13 = 26.638181697 k = 26.638181697 Simplifying k = 26.638181697Subproblem 2
k + -13 = -13.638181697 Simplifying k + -13 = -13.638181697 Reorder the terms: -13 + k = -13.638181697 Solving -13 + k = -13.638181697 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + k = -13.638181697 + 13 Combine like terms: -13 + 13 = 0 0 + k = -13.638181697 + 13 k = -13.638181697 + 13 Combine like terms: -13.638181697 + 13 = -0.638181697 k = -0.638181697 Simplifying k = -0.638181697Solution
The solution to the problem is based on the solutions from the subproblems. k = {26.638181697, -0.638181697}
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