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Simplifying k2 + 24k + 25 = 0 Reorder the terms: 25 + 24k + k2 = 0 Solving 25 + 24k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + 24k + -25 + k2 = 0 + -25 Reorder the terms: 25 + -25 + 24k + k2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 24k + k2 = 0 + -25 24k + k2 = 0 + -25 Combine like terms: 0 + -25 = -25 24k + k2 = -25 The k term is 24k. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24k + 144 + k2 = -25 + 144 Reorder the terms: 144 + 24k + k2 = -25 + 144 Combine like terms: -25 + 144 = 119 144 + 24k + k2 = 119 Factor a perfect square on the left side: (k + 12)(k + 12) = 119 Calculate the square root of the right side: 10.908712115 Break this problem into two subproblems by setting (k + 12) equal to 10.908712115 and -10.908712115.Subproblem 1
k + 12 = 10.908712115 Simplifying k + 12 = 10.908712115 Reorder the terms: 12 + k = 10.908712115 Solving 12 + k = 10.908712115 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + k = 10.908712115 + -12 Combine like terms: 12 + -12 = 0 0 + k = 10.908712115 + -12 k = 10.908712115 + -12 Combine like terms: 10.908712115 + -12 = -1.091287885 k = -1.091287885 Simplifying k = -1.091287885Subproblem 2
k + 12 = -10.908712115 Simplifying k + 12 = -10.908712115 Reorder the terms: 12 + k = -10.908712115 Solving 12 + k = -10.908712115 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + k = -10.908712115 + -12 Combine like terms: 12 + -12 = 0 0 + k = -10.908712115 + -12 k = -10.908712115 + -12 Combine like terms: -10.908712115 + -12 = -22.908712115 k = -22.908712115 Simplifying k = -22.908712115Solution
The solution to the problem is based on the solutions from the subproblems. k = {-1.091287885, -22.908712115}
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