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Simplifying k2 + -2k = 28 Reorder the terms: -2k + k2 = 28 Solving -2k + k2 = 28 Solving for variable 'k'. Reorder the terms: -28 + -2k + k2 = 28 + -28 Combine like terms: 28 + -28 = 0 -28 + -2k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + -2k + 28 + k2 = 0 + 28 Reorder the terms: -28 + 28 + -2k + k2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -2k + k2 = 0 + 28 -2k + k2 = 0 + 28 Combine like terms: 0 + 28 = 28 -2k + k2 = 28 The k term is -2k. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2k + 1 + k2 = 28 + 1 Reorder the terms: 1 + -2k + k2 = 28 + 1 Combine like terms: 28 + 1 = 29 1 + -2k + k2 = 29 Factor a perfect square on the left side: (k + -1)(k + -1) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (k + -1) equal to 5.385164807 and -5.385164807.Subproblem 1
k + -1 = 5.385164807 Simplifying k + -1 = 5.385164807 Reorder the terms: -1 + k = 5.385164807 Solving -1 + k = 5.385164807 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + k = 5.385164807 + 1 Combine like terms: -1 + 1 = 0 0 + k = 5.385164807 + 1 k = 5.385164807 + 1 Combine like terms: 5.385164807 + 1 = 6.385164807 k = 6.385164807 Simplifying k = 6.385164807Subproblem 2
k + -1 = -5.385164807 Simplifying k + -1 = -5.385164807 Reorder the terms: -1 + k = -5.385164807 Solving -1 + k = -5.385164807 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + k = -5.385164807 + 1 Combine like terms: -1 + 1 = 0 0 + k = -5.385164807 + 1 k = -5.385164807 + 1 Combine like terms: -5.385164807 + 1 = -4.385164807 k = -4.385164807 Simplifying k = -4.385164807Solution
The solution to the problem is based on the solutions from the subproblems. k = {6.385164807, -4.385164807}
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