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Simplifying 3.5K(K) + -1K = 45 Multiply K * K 3.5K2 + -1K = 45 Reorder the terms: -1K + 3.5K2 = 45 Solving -1K + 3.5K2 = 45 Solving for variable 'K'. Reorder the terms: -45 + -1K + 3.5K2 = 45 + -45 Combine like terms: 45 + -45 = 0 -45 + -1K + 3.5K2 = 0 Begin completing the square. Divide all terms by 3.5 the coefficient of the squared term: Divide each side by '3.5'. -12.85714286 + -0.2857142857K + K2 = 0 Move the constant term to the right: Add '12.85714286' to each side of the equation. -12.85714286 + -0.2857142857K + 12.85714286 + K2 = 0 + 12.85714286 Reorder the terms: -12.85714286 + 12.85714286 + -0.2857142857K + K2 = 0 + 12.85714286 Combine like terms: -12.85714286 + 12.85714286 = 0.00000000 0.00000000 + -0.2857142857K + K2 = 0 + 12.85714286 -0.2857142857K + K2 = 0 + 12.85714286 Combine like terms: 0 + 12.85714286 = 12.85714286 -0.2857142857K + K2 = 12.85714286 The K term is -0.2857142857K. Take half its coefficient (-0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. -0.2857142857K + 0.02040816328 + K2 = 12.85714286 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857K + K2 = 12.85714286 + 0.02040816328 Combine like terms: 12.85714286 + 0.02040816328 = 12.87755102328 0.02040816328 + -0.2857142857K + K2 = 12.87755102328 Factor a perfect square on the left side: (K + -0.1428571429)(K + -0.1428571429) = 12.87755102328 Calculate the square root of the right side: 3.588530482 Break this problem into two subproblems by setting (K + -0.1428571429) equal to 3.588530482 and -3.588530482.Subproblem 1
K + -0.1428571429 = 3.588530482 Simplifying K + -0.1428571429 = 3.588530482 Reorder the terms: -0.1428571429 + K = 3.588530482 Solving -0.1428571429 + K = 3.588530482 Solving for variable 'K'. Move all terms containing K to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + K = 3.588530482 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + K = 3.588530482 + 0.1428571429 K = 3.588530482 + 0.1428571429 Combine like terms: 3.588530482 + 0.1428571429 = 3.7313876249 K = 3.7313876249 Simplifying K = 3.7313876249Subproblem 2
K + -0.1428571429 = -3.588530482 Simplifying K + -0.1428571429 = -3.588530482 Reorder the terms: -0.1428571429 + K = -3.588530482 Solving -0.1428571429 + K = -3.588530482 Solving for variable 'K'. Move all terms containing K to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + K = -3.588530482 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + K = -3.588530482 + 0.1428571429 K = -3.588530482 + 0.1428571429 Combine like terms: -3.588530482 + 0.1428571429 = -3.4456733391 K = -3.4456733391 Simplifying K = -3.4456733391Solution
The solution to the problem is based on the solutions from the subproblems. K = {3.7313876249, -3.4456733391}
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