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Simplifying -4K2 + -8K + -3 = -5K2 Reorder the terms: -3 + -8K + -4K2 = -5K2 Solving -3 + -8K + -4K2 = -5K2 Solving for variable 'K'. Combine like terms: -4K2 + 5K2 = 1K2 -3 + -8K + 1K2 = -5K2 + 5K2 Combine like terms: -5K2 + 5K2 = 0 -3 + -8K + 1K2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -8K + 3 + K2 = 0 + 3 Reorder the terms: -3 + 3 + -8K + K2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -8K + K2 = 0 + 3 -8K + K2 = 0 + 3 Combine like terms: 0 + 3 = 3 -8K + K2 = 3 The K term is -8K. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8K + 16 + K2 = 3 + 16 Reorder the terms: 16 + -8K + K2 = 3 + 16 Combine like terms: 3 + 16 = 19 16 + -8K + K2 = 19 Factor a perfect square on the left side: (K + -4)(K + -4) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (K + -4) equal to 4.358898944 and -4.358898944.Subproblem 1
K + -4 = 4.358898944 Simplifying K + -4 = 4.358898944 Reorder the terms: -4 + K = 4.358898944 Solving -4 + K = 4.358898944 Solving for variable 'K'. Move all terms containing K to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + K = 4.358898944 + 4 Combine like terms: -4 + 4 = 0 0 + K = 4.358898944 + 4 K = 4.358898944 + 4 Combine like terms: 4.358898944 + 4 = 8.358898944 K = 8.358898944 Simplifying K = 8.358898944Subproblem 2
K + -4 = -4.358898944 Simplifying K + -4 = -4.358898944 Reorder the terms: -4 + K = -4.358898944 Solving -4 + K = -4.358898944 Solving for variable 'K'. Move all terms containing K to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + K = -4.358898944 + 4 Combine like terms: -4 + 4 = 0 0 + K = -4.358898944 + 4 K = -4.358898944 + 4 Combine like terms: -4.358898944 + 4 = -0.358898944 K = -0.358898944 Simplifying K = -0.358898944Solution
The solution to the problem is based on the solutions from the subproblems. K = {8.358898944, -0.358898944}
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