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Simplifying k2 + 15 = -14k Reorder the terms: 15 + k2 = -14k Solving 15 + k2 = -14k Solving for variable 'k'. Reorder the terms: 15 + 14k + k2 = -14k + 14k Combine like terms: -14k + 14k = 0 15 + 14k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + 14k + -15 + k2 = 0 + -15 Reorder the terms: 15 + -15 + 14k + k2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 14k + k2 = 0 + -15 14k + k2 = 0 + -15 Combine like terms: 0 + -15 = -15 14k + k2 = -15 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 = -15 + 49 Reorder the terms: 49 + 14k + k2 = -15 + 49 Combine like terms: -15 + 49 = 34 49 + 14k + k2 = 34 Factor a perfect square on the left side: (k + 7)(k + 7) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (k + 7) equal to 5.830951895 and -5.830951895.Subproblem 1
k + 7 = 5.830951895 Simplifying k + 7 = 5.830951895 Reorder the terms: 7 + k = 5.830951895 Solving 7 + k = 5.830951895 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 = 5.830951895 + -7 Combine like terms: 7 + -7 = 0 0 + k = 5.830951895 + -7 k = 5.830951895 + -7 Combine like terms: 5.830951895 + -7 = -1.169048105 k = -1.169048105 Simplifying k = -1.169048105Subproblem 2
k + 7 = -5.830951895 Simplifying k + 7 = -5.830951895 Reorder the terms: 7 + k = -5.830951895 Solving 7 + k = -5.830951895 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 = -5.830951895 + -7 Combine like terms: 7 + -7 = 0 0 + k = -5.830951895 + -7 k = -5.830951895 + -7 Combine like terms: -5.830951895 + -7 = -12.830951895 k = -12.830951895 Simplifying k = -12.830951895Solution
The solution to the problem is based on the solutions from the subproblems. k = {-1.169048105, -12.830951895}
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