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Simplifying k2 + -14k + -63 = 0 Reorder the terms: -63 + -14k + k2 = 0 Solving -63 + -14k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '63' to each side of the equation. -63 + -14k + 63 + k2 = 0 + 63 Reorder the terms: -63 + 63 + -14k + k2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + -14k + k2 = 0 + 63 -14k + k2 = 0 + 63 Combine like terms: 0 + 63 = 63 -14k + k2 = 63 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 = 63 + 49 Reorder the terms: 49 + -14k + k2 = 63 + 49 Combine like terms: 63 + 49 = 112 49 + -14k + k2 = 112 Factor a perfect square on the left side: (k + -7)(k + -7) = 112 Calculate the square root of the right side: 10.583005244 Break this problem into two subproblems by setting (k + -7) equal to 10.583005244 and -10.583005244.Subproblem 1
k + -7 = 10.583005244 Simplifying k + -7 = 10.583005244 Reorder the terms: -7 + k = 10.583005244 Solving -7 + k = 10.583005244 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 = 10.583005244 + 7 Combine like terms: -7 + 7 = 0 0 + k = 10.583005244 + 7 k = 10.583005244 + 7 Combine like terms: 10.583005244 + 7 = 17.583005244 k = 17.583005244 Simplifying k = 17.583005244Subproblem 2
k + -7 = -10.583005244 Simplifying k + -7 = -10.583005244 Reorder the terms: -7 + k = -10.583005244 Solving -7 + k = -10.583005244 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 = -10.583005244 + 7 Combine like terms: -7 + 7 = 0 0 + k = -10.583005244 + 7 k = -10.583005244 + 7 Combine like terms: -10.583005244 + 7 = -3.583005244 k = -3.583005244 Simplifying k = -3.583005244Solution
The solution to the problem is based on the solutions from the subproblems. k = {17.583005244, -3.583005244}
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