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Simplifying K2 + 4K + -24 = 0 Reorder the terms: -24 + 4K + K2 = 0 Solving -24 + 4K + K2 = 0 Solving for variable 'K'. Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + 4K + 24 + K2 = 0 + 24 Reorder the terms: -24 + 24 + 4K + K2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 4K + K2 = 0 + 24 4K + K2 = 0 + 24 Combine like terms: 0 + 24 = 24 4K + K2 = 24 The K term is 4K. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4K + 4 + K2 = 24 + 4 Reorder the terms: 4 + 4K + K2 = 24 + 4 Combine like terms: 24 + 4 = 28 4 + 4K + K2 = 28 Factor a perfect square on the left side: (K + 2)(K + 2) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (K + 2) equal to 5.291502622 and -5.291502622.Subproblem 1
K + 2 = 5.291502622 Simplifying K + 2 = 5.291502622 Reorder the terms: 2 + K = 5.291502622 Solving 2 + K = 5.291502622 Solving for variable 'K'. Move all terms containing K to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + K = 5.291502622 + -2 Combine like terms: 2 + -2 = 0 0 + K = 5.291502622 + -2 K = 5.291502622 + -2 Combine like terms: 5.291502622 + -2 = 3.291502622 K = 3.291502622 Simplifying K = 3.291502622Subproblem 2
K + 2 = -5.291502622 Simplifying K + 2 = -5.291502622 Reorder the terms: 2 + K = -5.291502622 Solving 2 + K = -5.291502622 Solving for variable 'K'. Move all terms containing K to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + K = -5.291502622 + -2 Combine like terms: 2 + -2 = 0 0 + K = -5.291502622 + -2 K = -5.291502622 + -2 Combine like terms: -5.291502622 + -2 = -7.291502622 K = -7.291502622 Simplifying K = -7.291502622Solution
The solution to the problem is based on the solutions from the subproblems. K = {3.291502622, -7.291502622}
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