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Simplifying k2 + -6k + -3 = 0 Reorder the terms: -3 + -6k + k2 = 0 Solving -3 + -6k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -6k + 3 + k2 = 0 + 3 Reorder the terms: -3 + 3 + -6k + k2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -6k + k2 = 0 + 3 -6k + k2 = 0 + 3 Combine like terms: 0 + 3 = 3 -6k + k2 = 3 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 = 3 + 9 Reorder the terms: 9 + -6k + k2 = 3 + 9 Combine like terms: 3 + 9 = 12 9 + -6k + k2 = 12 Factor a perfect square on the left side: (k + -3)(k + -3) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (k + -3) equal to 3.464101615 and -3.464101615.Subproblem 1
k + -3 = 3.464101615 Simplifying k + -3 = 3.464101615 Reorder the terms: -3 + k = 3.464101615 Solving -3 + k = 3.464101615 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 = 3.464101615 + 3 Combine like terms: -3 + 3 = 0 0 + k = 3.464101615 + 3 k = 3.464101615 + 3 Combine like terms: 3.464101615 + 3 = 6.464101615 k = 6.464101615 Simplifying k = 6.464101615Subproblem 2
k + -3 = -3.464101615 Simplifying k + -3 = -3.464101615 Reorder the terms: -3 + k = -3.464101615 Solving -3 + k = -3.464101615 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 = -3.464101615 + 3 Combine like terms: -3 + 3 = 0 0 + k = -3.464101615 + 3 k = -3.464101615 + 3 Combine like terms: -3.464101615 + 3 = -0.464101615 k = -0.464101615 Simplifying k = -0.464101615Solution
The solution to the problem is based on the solutions from the subproblems. k = {6.464101615, -0.464101615}
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