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Simplifying K2 + K = 200 Reorder the terms: K + K2 = 200 Solving K + K2 = 200 Solving for variable 'K'. Reorder the terms: -200 + K + K2 = 200 + -200 Combine like terms: 200 + -200 = 0 -200 + K + K2 = 0 Begin completing the square. Move the constant term to the right: Add '200' to each side of the equation. -200 + K + 200 + K2 = 0 + 200 Reorder the terms: -200 + 200 + K + K2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + K + K2 = 0 + 200 K + K2 = 0 + 200 Combine like terms: 0 + 200 = 200 K + K2 = 200 The K term is K. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. K + 0.25 + K2 = 200 + 0.25 Reorder the terms: 0.25 + K + K2 = 200 + 0.25 Combine like terms: 200 + 0.25 = 200.25 0.25 + K + K2 = 200.25 Factor a perfect square on the left side: (K + 0.5)(K + 0.5) = 200.25 Calculate the square root of the right side: 14.150971698 Break this problem into two subproblems by setting (K + 0.5) equal to 14.150971698 and -14.150971698.Subproblem 1
K + 0.5 = 14.150971698 Simplifying K + 0.5 = 14.150971698 Reorder the terms: 0.5 + K = 14.150971698 Solving 0.5 + K = 14.150971698 Solving for variable 'K'. Move all terms containing K to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + K = 14.150971698 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + K = 14.150971698 + -0.5 K = 14.150971698 + -0.5 Combine like terms: 14.150971698 + -0.5 = 13.650971698 K = 13.650971698 Simplifying K = 13.650971698Subproblem 2
K + 0.5 = -14.150971698 Simplifying K + 0.5 = -14.150971698 Reorder the terms: 0.5 + K = -14.150971698 Solving 0.5 + K = -14.150971698 Solving for variable 'K'. Move all terms containing K to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + K = -14.150971698 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + K = -14.150971698 + -0.5 K = -14.150971698 + -0.5 Combine like terms: -14.150971698 + -0.5 = -14.650971698 K = -14.650971698 Simplifying K = -14.650971698Solution
The solution to the problem is based on the solutions from the subproblems. K = {13.650971698, -14.650971698}
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