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Simplifying k2 + -6k = 20 Reorder the terms: -6k + k2 = 20 Solving -6k + k2 = 20 Solving for variable 'k'. Reorder the terms: -20 + -6k + k2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + -6k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + -6k + 20 + k2 = 0 + 20 Reorder the terms: -20 + 20 + -6k + k2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -6k + k2 = 0 + 20 -6k + k2 = 0 + 20 Combine like terms: 0 + 20 = 20 -6k + k2 = 20 The k term is -6k. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6k + 9 + k2 = 20 + 9 Reorder the terms: 9 + -6k + k2 = 20 + 9 Combine like terms: 20 + 9 = 29 9 + -6k + k2 = 29 Factor a perfect square on the left side: (k + -3)(k + -3) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (k + -3) equal to 5.385164807 and -5.385164807.Subproblem 1
k + -3 = 5.385164807 Simplifying k + -3 = 5.385164807 Reorder the terms: -3 + k = 5.385164807 Solving -3 + k = 5.385164807 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + k = 5.385164807 + 3 Combine like terms: -3 + 3 = 0 0 + k = 5.385164807 + 3 k = 5.385164807 + 3 Combine like terms: 5.385164807 + 3 = 8.385164807 k = 8.385164807 Simplifying k = 8.385164807Subproblem 2
k + -3 = -5.385164807 Simplifying k + -3 = -5.385164807 Reorder the terms: -3 + k = -5.385164807 Solving -3 + k = -5.385164807 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + k = -5.385164807 + 3 Combine like terms: -3 + 3 = 0 0 + k = -5.385164807 + 3 k = -5.385164807 + 3 Combine like terms: -5.385164807 + 3 = -2.385164807 k = -2.385164807 Simplifying k = -2.385164807Solution
The solution to the problem is based on the solutions from the subproblems. k = {8.385164807, -2.385164807}
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