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Simplifying k2 = 55 + -2k Solving k2 = 55 + -2k Solving for variable 'k'. Reorder the terms: -55 + 2k + k2 = 55 + -2k + -55 + 2k Reorder the terms: -55 + 2k + k2 = 55 + -55 + -2k + 2k Combine like terms: 55 + -55 = 0 -55 + 2k + k2 = 0 + -2k + 2k -55 + 2k + k2 = -2k + 2k Combine like terms: -2k + 2k = 0 -55 + 2k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '55' to each side of the equation. -55 + 2k + 55 + k2 = 0 + 55 Reorder the terms: -55 + 55 + 2k + k2 = 0 + 55 Combine like terms: -55 + 55 = 0 0 + 2k + k2 = 0 + 55 2k + k2 = 0 + 55 Combine like terms: 0 + 55 = 55 2k + k2 = 55 The k term is 2k. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2k + 1 + k2 = 55 + 1 Reorder the terms: 1 + 2k + k2 = 55 + 1 Combine like terms: 55 + 1 = 56 1 + 2k + k2 = 56 Factor a perfect square on the left side: (k + 1)(k + 1) = 56 Calculate the square root of the right side: 7.483314774 Break this problem into two subproblems by setting (k + 1) equal to 7.483314774 and -7.483314774.Subproblem 1
k + 1 = 7.483314774 Simplifying k + 1 = 7.483314774 Reorder the terms: 1 + k = 7.483314774 Solving 1 + k = 7.483314774 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + k = 7.483314774 + -1 Combine like terms: 1 + -1 = 0 0 + k = 7.483314774 + -1 k = 7.483314774 + -1 Combine like terms: 7.483314774 + -1 = 6.483314774 k = 6.483314774 Simplifying k = 6.483314774Subproblem 2
k + 1 = -7.483314774 Simplifying k + 1 = -7.483314774 Reorder the terms: 1 + k = -7.483314774 Solving 1 + k = -7.483314774 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + k = -7.483314774 + -1 Combine like terms: 1 + -1 = 0 0 + k = -7.483314774 + -1 k = -7.483314774 + -1 Combine like terms: -7.483314774 + -1 = -8.483314774 k = -8.483314774 Simplifying k = -8.483314774Solution
The solution to the problem is based on the solutions from the subproblems. k = {6.483314774, -8.483314774}
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