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Simplifying k2 + -6k + 2 = 0 Reorder the terms: 2 + -6k + k2 = 0 Solving 2 + -6k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -6k + -2 + k2 = 0 + -2 Reorder the terms: 2 + -2 + -6k + k2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -6k + k2 = 0 + -2 -6k + k2 = 0 + -2 Combine like terms: 0 + -2 = -2 -6k + k2 = -2 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 = -2 + 9 Reorder the terms: 9 + -6k + k2 = -2 + 9 Combine like terms: -2 + 9 = 7 9 + -6k + k2 = 7 Factor a perfect square on the left side: (k + -3)(k + -3) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (k + -3) equal to 2.645751311 and -2.645751311.Subproblem 1
k + -3 = 2.645751311 Simplifying k + -3 = 2.645751311 Reorder the terms: -3 + k = 2.645751311 Solving -3 + k = 2.645751311 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 = 2.645751311 + 3 Combine like terms: -3 + 3 = 0 0 + k = 2.645751311 + 3 k = 2.645751311 + 3 Combine like terms: 2.645751311 + 3 = 5.645751311 k = 5.645751311 Simplifying k = 5.645751311Subproblem 2
k + -3 = -2.645751311 Simplifying k + -3 = -2.645751311 Reorder the terms: -3 + k = -2.645751311 Solving -3 + k = -2.645751311 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 = -2.645751311 + 3 Combine like terms: -3 + 3 = 0 0 + k = -2.645751311 + 3 k = -2.645751311 + 3 Combine like terms: -2.645751311 + 3 = 0.354248689 k = 0.354248689 Simplifying k = 0.354248689Solution
The solution to the problem is based on the solutions from the subproblems. k = {5.645751311, 0.354248689}
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