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Simplifying k2 + 2k + -60 = 0 Reorder the terms: -60 + 2k + k2 = 0 Solving -60 + 2k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + 2k + 60 + k2 = 0 + 60 Reorder the terms: -60 + 60 + 2k + k2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 2k + k2 = 0 + 60 2k + k2 = 0 + 60 Combine like terms: 0 + 60 = 60 2k + k2 = 60 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 = 60 + 1 Reorder the terms: 1 + 2k + k2 = 60 + 1 Combine like terms: 60 + 1 = 61 1 + 2k + k2 = 61 Factor a perfect square on the left side: (k + 1)(k + 1) = 61 Calculate the square root of the right side: 7.810249676 Break this problem into two subproblems by setting (k + 1) equal to 7.810249676 and -7.810249676.Subproblem 1
k + 1 = 7.810249676 Simplifying k + 1 = 7.810249676 Reorder the terms: 1 + k = 7.810249676 Solving 1 + k = 7.810249676 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 = 7.810249676 + -1 Combine like terms: 1 + -1 = 0 0 + k = 7.810249676 + -1 k = 7.810249676 + -1 Combine like terms: 7.810249676 + -1 = 6.810249676 k = 6.810249676 Simplifying k = 6.810249676Subproblem 2
k + 1 = -7.810249676 Simplifying k + 1 = -7.810249676 Reorder the terms: 1 + k = -7.810249676 Solving 1 + k = -7.810249676 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 = -7.810249676 + -1 Combine like terms: 1 + -1 = 0 0 + k = -7.810249676 + -1 k = -7.810249676 + -1 Combine like terms: -7.810249676 + -1 = -8.810249676 k = -8.810249676 Simplifying k = -8.810249676Solution
The solution to the problem is based on the solutions from the subproblems. k = {6.810249676, -8.810249676}
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