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Simplifying -1k2 + 6k + 1 = 0 Reorder the terms: 1 + 6k + -1k2 = 0 Solving 1 + 6k + -1k2 = 0 Solving for variable 'k'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1 + -6k + k2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -6k + 1 + k2 = 0 + 1 Reorder the terms: -1 + 1 + -6k + k2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -6k + k2 = 0 + 1 -6k + k2 = 0 + 1 Combine like terms: 0 + 1 = 1 -6k + k2 = 1 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 = 1 + 9 Reorder the terms: 9 + -6k + k2 = 1 + 9 Combine like terms: 1 + 9 = 10 9 + -6k + k2 = 10 Factor a perfect square on the left side: (k + -3)(k + -3) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (k + -3) equal to 3.16227766 and -3.16227766.Subproblem 1
k + -3 = 3.16227766 Simplifying k + -3 = 3.16227766 Reorder the terms: -3 + k = 3.16227766 Solving -3 + k = 3.16227766 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 = 3.16227766 + 3 Combine like terms: -3 + 3 = 0 0 + k = 3.16227766 + 3 k = 3.16227766 + 3 Combine like terms: 3.16227766 + 3 = 6.16227766 k = 6.16227766 Simplifying k = 6.16227766Subproblem 2
k + -3 = -3.16227766 Simplifying k + -3 = -3.16227766 Reorder the terms: -3 + k = -3.16227766 Solving -3 + k = -3.16227766 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 = -3.16227766 + 3 Combine like terms: -3 + 3 = 0 0 + k = -3.16227766 + 3 k = -3.16227766 + 3 Combine like terms: -3.16227766 + 3 = -0.16227766 k = -0.16227766 Simplifying k = -0.16227766Solution
The solution to the problem is based on the solutions from the subproblems. k = {6.16227766, -0.16227766}
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