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Simplifying k2 + -26k + 49 = 0 Reorder the terms: 49 + -26k + k2 = 0 Solving 49 + -26k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '-49' to each side of the equation. 49 + -26k + -49 + k2 = 0 + -49 Reorder the terms: 49 + -49 + -26k + k2 = 0 + -49 Combine like terms: 49 + -49 = 0 0 + -26k + k2 = 0 + -49 -26k + k2 = 0 + -49 Combine like terms: 0 + -49 = -49 -26k + k2 = -49 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 = -49 + 169 Reorder the terms: 169 + -26k + k2 = -49 + 169 Combine like terms: -49 + 169 = 120 169 + -26k + k2 = 120 Factor a perfect square on the left side: (k + -13)(k + -13) = 120 Calculate the square root of the right side: 10.95445115 Break this problem into two subproblems by setting (k + -13) equal to 10.95445115 and -10.95445115.Subproblem 1
k + -13 = 10.95445115 Simplifying k + -13 = 10.95445115 Reorder the terms: -13 + k = 10.95445115 Solving -13 + k = 10.95445115 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 = 10.95445115 + 13 Combine like terms: -13 + 13 = 0 0 + k = 10.95445115 + 13 k = 10.95445115 + 13 Combine like terms: 10.95445115 + 13 = 23.95445115 k = 23.95445115 Simplifying k = 23.95445115Subproblem 2
k + -13 = -10.95445115 Simplifying k + -13 = -10.95445115 Reorder the terms: -13 + k = -10.95445115 Solving -13 + k = -10.95445115 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 = -10.95445115 + 13 Combine like terms: -13 + 13 = 0 0 + k = -10.95445115 + 13 k = -10.95445115 + 13 Combine like terms: -10.95445115 + 13 = 2.04554885 k = 2.04554885 Simplifying k = 2.04554885Solution
The solution to the problem is based on the solutions from the subproblems. k = {23.95445115, 2.04554885}
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