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Simplifying k2 + -5k + -69 = 0 Reorder the terms: -69 + -5k + k2 = 0 Solving -69 + -5k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '69' to each side of the equation. -69 + -5k + 69 + k2 = 0 + 69 Reorder the terms: -69 + 69 + -5k + k2 = 0 + 69 Combine like terms: -69 + 69 = 0 0 + -5k + k2 = 0 + 69 -5k + k2 = 0 + 69 Combine like terms: 0 + 69 = 69 -5k + k2 = 69 The k term is -5k. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5k + 6.25 + k2 = 69 + 6.25 Reorder the terms: 6.25 + -5k + k2 = 69 + 6.25 Combine like terms: 69 + 6.25 = 75.25 6.25 + -5k + k2 = 75.25 Factor a perfect square on the left side: (k + -2.5)(k + -2.5) = 75.25 Calculate the square root of the right side: 8.674675786 Break this problem into two subproblems by setting (k + -2.5) equal to 8.674675786 and -8.674675786.Subproblem 1
k + -2.5 = 8.674675786 Simplifying k + -2.5 = 8.674675786 Reorder the terms: -2.5 + k = 8.674675786 Solving -2.5 + k = 8.674675786 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + k = 8.674675786 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + k = 8.674675786 + 2.5 k = 8.674675786 + 2.5 Combine like terms: 8.674675786 + 2.5 = 11.174675786 k = 11.174675786 Simplifying k = 11.174675786Subproblem 2
k + -2.5 = -8.674675786 Simplifying k + -2.5 = -8.674675786 Reorder the terms: -2.5 + k = -8.674675786 Solving -2.5 + k = -8.674675786 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + k = -8.674675786 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + k = -8.674675786 + 2.5 k = -8.674675786 + 2.5 Combine like terms: -8.674675786 + 2.5 = -6.174675786 k = -6.174675786 Simplifying k = -6.174675786Solution
The solution to the problem is based on the solutions from the subproblems. k = {11.174675786, -6.174675786}
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