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Simplifying k2 + -2k + -52 = 0 Reorder the terms: -52 + -2k + k2 = 0 Solving -52 + -2k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '52' to each side of the equation. -52 + -2k + 52 + k2 = 0 + 52 Reorder the terms: -52 + 52 + -2k + k2 = 0 + 52 Combine like terms: -52 + 52 = 0 0 + -2k + k2 = 0 + 52 -2k + k2 = 0 + 52 Combine like terms: 0 + 52 = 52 -2k + k2 = 52 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 = 52 + 1 Reorder the terms: 1 + -2k + k2 = 52 + 1 Combine like terms: 52 + 1 = 53 1 + -2k + k2 = 53 Factor a perfect square on the left side: (k + -1)(k + -1) = 53 Calculate the square root of the right side: 7.280109889 Break this problem into two subproblems by setting (k + -1) equal to 7.280109889 and -7.280109889.Subproblem 1
k + -1 = 7.280109889 Simplifying k + -1 = 7.280109889 Reorder the terms: -1 + k = 7.280109889 Solving -1 + k = 7.280109889 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 = 7.280109889 + 1 Combine like terms: -1 + 1 = 0 0 + k = 7.280109889 + 1 k = 7.280109889 + 1 Combine like terms: 7.280109889 + 1 = 8.280109889 k = 8.280109889 Simplifying k = 8.280109889Subproblem 2
k + -1 = -7.280109889 Simplifying k + -1 = -7.280109889 Reorder the terms: -1 + k = -7.280109889 Solving -1 + k = -7.280109889 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 = -7.280109889 + 1 Combine like terms: -1 + 1 = 0 0 + k = -7.280109889 + 1 k = -7.280109889 + 1 Combine like terms: -7.280109889 + 1 = -6.280109889 k = -6.280109889 Simplifying k = -6.280109889Solution
The solution to the problem is based on the solutions from the subproblems. k = {8.280109889, -6.280109889}
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