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Simplifying (K + 5)(K + 2) = 44 Reorder the terms: (5 + K)(K + 2) = 44 Reorder the terms: (5 + K)(2 + K) = 44 Multiply (5 + K) * (2 + K) (5(2 + K) + K(2 + K)) = 44 ((2 * 5 + K * 5) + K(2 + K)) = 44 ((10 + 5K) + K(2 + K)) = 44 (10 + 5K + (2 * K + K * K)) = 44 (10 + 5K + (2K + K2)) = 44 Combine like terms: 5K + 2K = 7K (10 + 7K + K2) = 44 Solving 10 + 7K + K2 = 44 Solving for variable 'K'. Reorder the terms: 10 + -44 + 7K + K2 = 44 + -44 Combine like terms: 10 + -44 = -34 -34 + 7K + K2 = 44 + -44 Combine like terms: 44 + -44 = 0 -34 + 7K + K2 = 0 Begin completing the square. Move the constant term to the right: Add '34' to each side of the equation. -34 + 7K + 34 + K2 = 0 + 34 Reorder the terms: -34 + 34 + 7K + K2 = 0 + 34 Combine like terms: -34 + 34 = 0 0 + 7K + K2 = 0 + 34 7K + K2 = 0 + 34 Combine like terms: 0 + 34 = 34 7K + K2 = 34 The K term is 7K. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7K + 12.25 + K2 = 34 + 12.25 Reorder the terms: 12.25 + 7K + K2 = 34 + 12.25 Combine like terms: 34 + 12.25 = 46.25 12.25 + 7K + K2 = 46.25 Factor a perfect square on the left side: (K + 3.5)(K + 3.5) = 46.25 Calculate the square root of the right side: 6.800735254 Break this problem into two subproblems by setting (K + 3.5) equal to 6.800735254 and -6.800735254.Subproblem 1
K + 3.5 = 6.800735254 Simplifying K + 3.5 = 6.800735254 Reorder the terms: 3.5 + K = 6.800735254 Solving 3.5 + K = 6.800735254 Solving for variable 'K'. Move all terms containing K to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + K = 6.800735254 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + K = 6.800735254 + -3.5 K = 6.800735254 + -3.5 Combine like terms: 6.800735254 + -3.5 = 3.300735254 K = 3.300735254 Simplifying K = 3.300735254Subproblem 2
K + 3.5 = -6.800735254 Simplifying K + 3.5 = -6.800735254 Reorder the terms: 3.5 + K = -6.800735254 Solving 3.5 + K = -6.800735254 Solving for variable 'K'. Move all terms containing K to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + K = -6.800735254 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + K = -6.800735254 + -3.5 K = -6.800735254 + -3.5 Combine like terms: -6.800735254 + -3.5 = -10.300735254 K = -10.300735254 Simplifying K = -10.300735254Solution
The solution to the problem is based on the solutions from the subproblems. K = {3.300735254, -10.300735254}
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