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Simplifying k2 + -28k + -1 = 0 Reorder the terms: -1 + -28k + k2 = 0 Solving -1 + -28k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -28k + 1 + k2 = 0 + 1 Reorder the terms: -1 + 1 + -28k + k2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -28k + k2 = 0 + 1 -28k + k2 = 0 + 1 Combine like terms: 0 + 1 = 1 -28k + k2 = 1 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 = 1 + 196 Reorder the terms: 196 + -28k + k2 = 1 + 196 Combine like terms: 1 + 196 = 197 196 + -28k + k2 = 197 Factor a perfect square on the left side: (k + -14)(k + -14) = 197 Calculate the square root of the right side: 14.035668848 Break this problem into two subproblems by setting (k + -14) equal to 14.035668848 and -14.035668848.Subproblem 1
k + -14 = 14.035668848 Simplifying k + -14 = 14.035668848 Reorder the terms: -14 + k = 14.035668848 Solving -14 + k = 14.035668848 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 = 14.035668848 + 14 Combine like terms: -14 + 14 = 0 0 + k = 14.035668848 + 14 k = 14.035668848 + 14 Combine like terms: 14.035668848 + 14 = 28.035668848 k = 28.035668848 Simplifying k = 28.035668848Subproblem 2
k + -14 = -14.035668848 Simplifying k + -14 = -14.035668848 Reorder the terms: -14 + k = -14.035668848 Solving -14 + k = -14.035668848 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 = -14.035668848 + 14 Combine like terms: -14 + 14 = 0 0 + k = -14.035668848 + 14 k = -14.035668848 + 14 Combine like terms: -14.035668848 + 14 = -0.035668848 k = -0.035668848 Simplifying k = -0.035668848Solution
The solution to the problem is based on the solutions from the subproblems. k = {28.035668848, -0.035668848}
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