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Simplifying k2 + -6k + -9 = 0 Reorder the terms: -9 + -6k + k2 = 0 Solving -9 + -6k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -6k + 9 + k2 = 0 + 9 Reorder the terms: -9 + 9 + -6k + k2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -6k + k2 = 0 + 9 -6k + k2 = 0 + 9 Combine like terms: 0 + 9 = 9 -6k + k2 = 9 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 = 9 + 9 Reorder the terms: 9 + -6k + k2 = 9 + 9 Combine like terms: 9 + 9 = 18 9 + -6k + k2 = 18 Factor a perfect square on the left side: (k + -3)(k + -3) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (k + -3) equal to 4.242640687 and -4.242640687.Subproblem 1
k + -3 = 4.242640687 Simplifying k + -3 = 4.242640687 Reorder the terms: -3 + k = 4.242640687 Solving -3 + k = 4.242640687 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 = 4.242640687 + 3 Combine like terms: -3 + 3 = 0 0 + k = 4.242640687 + 3 k = 4.242640687 + 3 Combine like terms: 4.242640687 + 3 = 7.242640687 k = 7.242640687 Simplifying k = 7.242640687Subproblem 2
k + -3 = -4.242640687 Simplifying k + -3 = -4.242640687 Reorder the terms: -3 + k = -4.242640687 Solving -3 + k = -4.242640687 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 = -4.242640687 + 3 Combine like terms: -3 + 3 = 0 0 + k = -4.242640687 + 3 k = -4.242640687 + 3 Combine like terms: -4.242640687 + 3 = -1.242640687 k = -1.242640687 Simplifying k = -1.242640687Solution
The solution to the problem is based on the solutions from the subproblems. k = {7.242640687, -1.242640687}
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