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Simplifying k2 + 2k + -50 = 0 Reorder the terms: -50 + 2k + k2 = 0 Solving -50 + 2k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + 2k + 50 + k2 = 0 + 50 Reorder the terms: -50 + 50 + 2k + k2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 2k + k2 = 0 + 50 2k + k2 = 0 + 50 Combine like terms: 0 + 50 = 50 2k + k2 = 50 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 = 50 + 1 Reorder the terms: 1 + 2k + k2 = 50 + 1 Combine like terms: 50 + 1 = 51 1 + 2k + k2 = 51 Factor a perfect square on the left side: (k + 1)(k + 1) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (k + 1) equal to 7.141428429 and -7.141428429.Subproblem 1
k + 1 = 7.141428429 Simplifying k + 1 = 7.141428429 Reorder the terms: 1 + k = 7.141428429 Solving 1 + k = 7.141428429 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 = 7.141428429 + -1 Combine like terms: 1 + -1 = 0 0 + k = 7.141428429 + -1 k = 7.141428429 + -1 Combine like terms: 7.141428429 + -1 = 6.141428429 k = 6.141428429 Simplifying k = 6.141428429Subproblem 2
k + 1 = -7.141428429 Simplifying k + 1 = -7.141428429 Reorder the terms: 1 + k = -7.141428429 Solving 1 + k = -7.141428429 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 = -7.141428429 + -1 Combine like terms: 1 + -1 = 0 0 + k = -7.141428429 + -1 k = -7.141428429 + -1 Combine like terms: -7.141428429 + -1 = -8.141428429 k = -8.141428429 Simplifying k = -8.141428429Solution
The solution to the problem is based on the solutions from the subproblems. k = {6.141428429, -8.141428429}
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