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Simplifying k2 + -6k + -143 = 0 Reorder the terms: -143 + -6k + k2 = 0 Solving -143 + -6k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '143' to each side of the equation. -143 + -6k + 143 + k2 = 0 + 143 Reorder the terms: -143 + 143 + -6k + k2 = 0 + 143 Combine like terms: -143 + 143 = 0 0 + -6k + k2 = 0 + 143 -6k + k2 = 0 + 143 Combine like terms: 0 + 143 = 143 -6k + k2 = 143 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 = 143 + 9 Reorder the terms: 9 + -6k + k2 = 143 + 9 Combine like terms: 143 + 9 = 152 9 + -6k + k2 = 152 Factor a perfect square on the left side: (k + -3)(k + -3) = 152 Calculate the square root of the right side: 12.328828006 Break this problem into two subproblems by setting (k + -3) equal to 12.328828006 and -12.328828006.Subproblem 1
k + -3 = 12.328828006 Simplifying k + -3 = 12.328828006 Reorder the terms: -3 + k = 12.328828006 Solving -3 + k = 12.328828006 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 = 12.328828006 + 3 Combine like terms: -3 + 3 = 0 0 + k = 12.328828006 + 3 k = 12.328828006 + 3 Combine like terms: 12.328828006 + 3 = 15.328828006 k = 15.328828006 Simplifying k = 15.328828006Subproblem 2
k + -3 = -12.328828006 Simplifying k + -3 = -12.328828006 Reorder the terms: -3 + k = -12.328828006 Solving -3 + k = -12.328828006 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 = -12.328828006 + 3 Combine like terms: -3 + 3 = 0 0 + k = -12.328828006 + 3 k = -12.328828006 + 3 Combine like terms: -12.328828006 + 3 = -9.328828006 k = -9.328828006 Simplifying k = -9.328828006Solution
The solution to the problem is based on the solutions from the subproblems. k = {15.328828006, -9.328828006}
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