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Simplifying k2 + -28k + -13 = 0 Reorder the terms: -13 + -28k + k2 = 0 Solving -13 + -28k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + -28k + 13 + k2 = 0 + 13 Reorder the terms: -13 + 13 + -28k + k2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -28k + k2 = 0 + 13 -28k + k2 = 0 + 13 Combine like terms: 0 + 13 = 13 -28k + k2 = 13 The k term is -28k. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28k + 196 + k2 = 13 + 196 Reorder the terms: 196 + -28k + k2 = 13 + 196 Combine like terms: 13 + 196 = 209 196 + -28k + k2 = 209 Factor a perfect square on the left side: (k + -14)(k + -14) = 209 Calculate the square root of the right side: 14.456832295 Break this problem into two subproblems by setting (k + -14) equal to 14.456832295 and -14.456832295.Subproblem 1
k + -14 = 14.456832295 Simplifying k + -14 = 14.456832295 Reorder the terms: -14 + k = 14.456832295 Solving -14 + k = 14.456832295 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + k = 14.456832295 + 14 Combine like terms: -14 + 14 = 0 0 + k = 14.456832295 + 14 k = 14.456832295 + 14 Combine like terms: 14.456832295 + 14 = 28.456832295 k = 28.456832295 Simplifying k = 28.456832295Subproblem 2
k + -14 = -14.456832295 Simplifying k + -14 = -14.456832295 Reorder the terms: -14 + k = -14.456832295 Solving -14 + k = -14.456832295 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + k = -14.456832295 + 14 Combine like terms: -14 + 14 = 0 0 + k = -14.456832295 + 14 k = -14.456832295 + 14 Combine like terms: -14.456832295 + 14 = -0.456832295 k = -0.456832295 Simplifying k = -0.456832295Solution
The solution to the problem is based on the solutions from the subproblems. k = {28.456832295, -0.456832295}
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