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Simplifying k2 + 2k = 25 Reorder the terms: 2k + k2 = 25 Solving 2k + k2 = 25 Solving for variable 'k'. Reorder the terms: -25 + 2k + k2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + 2k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + 2k + 25 + k2 = 0 + 25 Reorder the terms: -25 + 25 + 2k + k2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 2k + k2 = 0 + 25 2k + k2 = 0 + 25 Combine like terms: 0 + 25 = 25 2k + k2 = 25 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 = 25 + 1 Reorder the terms: 1 + 2k + k2 = 25 + 1 Combine like terms: 25 + 1 = 26 1 + 2k + k2 = 26 Factor a perfect square on the left side: (k + 1)(k + 1) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (k + 1) equal to 5.099019514 and -5.099019514.Subproblem 1
k + 1 = 5.099019514 Simplifying k + 1 = 5.099019514 Reorder the terms: 1 + k = 5.099019514 Solving 1 + k = 5.099019514 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 = 5.099019514 + -1 Combine like terms: 1 + -1 = 0 0 + k = 5.099019514 + -1 k = 5.099019514 + -1 Combine like terms: 5.099019514 + -1 = 4.099019514 k = 4.099019514 Simplifying k = 4.099019514Subproblem 2
k + 1 = -5.099019514 Simplifying k + 1 = -5.099019514 Reorder the terms: 1 + k = -5.099019514 Solving 1 + k = -5.099019514 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 = -5.099019514 + -1 Combine like terms: 1 + -1 = 0 0 + k = -5.099019514 + -1 k = -5.099019514 + -1 Combine like terms: -5.099019514 + -1 = -6.099019514 k = -6.099019514 Simplifying k = -6.099019514Solution
The solution to the problem is based on the solutions from the subproblems. k = {4.099019514, -6.099019514}
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