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Simplifying K2 + -24K + 16 = 0 Reorder the terms: 16 + -24K + K2 = 0 Solving 16 + -24K + K2 = 0 Solving for variable 'K'. Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + -24K + -16 + K2 = 0 + -16 Reorder the terms: 16 + -16 + -24K + K2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -24K + K2 = 0 + -16 -24K + K2 = 0 + -16 Combine like terms: 0 + -16 = -16 -24K + K2 = -16 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 = -16 + 144 Reorder the terms: 144 + -24K + K2 = -16 + 144 Combine like terms: -16 + 144 = 128 144 + -24K + K2 = 128 Factor a perfect square on the left side: (K + -12)(K + -12) = 128 Calculate the square root of the right side: 11.313708499 Break this problem into two subproblems by setting (K + -12) equal to 11.313708499 and -11.313708499.Subproblem 1
K + -12 = 11.313708499 Simplifying K + -12 = 11.313708499 Reorder the terms: -12 + K = 11.313708499 Solving -12 + K = 11.313708499 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 = 11.313708499 + 12 Combine like terms: -12 + 12 = 0 0 + K = 11.313708499 + 12 K = 11.313708499 + 12 Combine like terms: 11.313708499 + 12 = 23.313708499 K = 23.313708499 Simplifying K = 23.313708499Subproblem 2
K + -12 = -11.313708499 Simplifying K + -12 = -11.313708499 Reorder the terms: -12 + K = -11.313708499 Solving -12 + K = -11.313708499 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 = -11.313708499 + 12 Combine like terms: -12 + 12 = 0 0 + K = -11.313708499 + 12 K = -11.313708499 + 12 Combine like terms: -11.313708499 + 12 = 0.686291501 K = 0.686291501 Simplifying K = 0.686291501Solution
The solution to the problem is based on the solutions from the subproblems. K = {23.313708499, 0.686291501}
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