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Simplifying k2 + -8k + -66 = 0 Reorder the terms: -66 + -8k + k2 = 0 Solving -66 + -8k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '66' to each side of the equation. -66 + -8k + 66 + k2 = 0 + 66 Reorder the terms: -66 + 66 + -8k + k2 = 0 + 66 Combine like terms: -66 + 66 = 0 0 + -8k + k2 = 0 + 66 -8k + k2 = 0 + 66 Combine like terms: 0 + 66 = 66 -8k + k2 = 66 The k term is -8k. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8k + 16 + k2 = 66 + 16 Reorder the terms: 16 + -8k + k2 = 66 + 16 Combine like terms: 66 + 16 = 82 16 + -8k + k2 = 82 Factor a perfect square on the left side: (k + -4)(k + -4) = 82 Calculate the square root of the right side: 9.055385138 Break this problem into two subproblems by setting (k + -4) equal to 9.055385138 and -9.055385138.Subproblem 1
k + -4 = 9.055385138 Simplifying k + -4 = 9.055385138 Reorder the terms: -4 + k = 9.055385138 Solving -4 + k = 9.055385138 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + k = 9.055385138 + 4 Combine like terms: -4 + 4 = 0 0 + k = 9.055385138 + 4 k = 9.055385138 + 4 Combine like terms: 9.055385138 + 4 = 13.055385138 k = 13.055385138 Simplifying k = 13.055385138Subproblem 2
k + -4 = -9.055385138 Simplifying k + -4 = -9.055385138 Reorder the terms: -4 + k = -9.055385138 Solving -4 + k = -9.055385138 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + k = -9.055385138 + 4 Combine like terms: -4 + 4 = 0 0 + k = -9.055385138 + 4 k = -9.055385138 + 4 Combine like terms: -9.055385138 + 4 = -5.055385138 k = -5.055385138 Simplifying k = -5.055385138Solution
The solution to the problem is based on the solutions from the subproblems. k = {13.055385138, -5.055385138}
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