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Simplifying k2 + -14k + -6 = -8 Reorder the terms: -6 + -14k + k2 = -8 Solving -6 + -14k + k2 = -8 Solving for variable 'k'. Reorder the terms: -6 + 8 + -14k + k2 = -8 + 8 Combine like terms: -6 + 8 = 2 2 + -14k + k2 = -8 + 8 Combine like terms: -8 + 8 = 0 2 + -14k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -14k + -2 + k2 = 0 + -2 Reorder the terms: 2 + -2 + -14k + k2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -14k + k2 = 0 + -2 -14k + k2 = 0 + -2 Combine like terms: 0 + -2 = -2 -14k + k2 = -2 The k term is -14k. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14k + 49 + k2 = -2 + 49 Reorder the terms: 49 + -14k + k2 = -2 + 49 Combine like terms: -2 + 49 = 47 49 + -14k + k2 = 47 Factor a perfect square on the left side: (k + -7)(k + -7) = 47 Calculate the square root of the right side: 6.8556546 Break this problem into two subproblems by setting (k + -7) equal to 6.8556546 and -6.8556546.Subproblem 1
k + -7 = 6.8556546 Simplifying k + -7 = 6.8556546 Reorder the terms: -7 + k = 6.8556546 Solving -7 + k = 6.8556546 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + k = 6.8556546 + 7 Combine like terms: -7 + 7 = 0 0 + k = 6.8556546 + 7 k = 6.8556546 + 7 Combine like terms: 6.8556546 + 7 = 13.8556546 k = 13.8556546 Simplifying k = 13.8556546Subproblem 2
k + -7 = -6.8556546 Simplifying k + -7 = -6.8556546 Reorder the terms: -7 + k = -6.8556546 Solving -7 + k = -6.8556546 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + k = -6.8556546 + 7 Combine like terms: -7 + 7 = 0 0 + k = -6.8556546 + 7 k = -6.8556546 + 7 Combine like terms: -6.8556546 + 7 = 0.1443454 k = 0.1443454 Simplifying k = 0.1443454Solution
The solution to the problem is based on the solutions from the subproblems. k = {13.8556546, 0.1443454}
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