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Simplifying K2 + -3K + -25 = 0 Reorder the terms: -25 + -3K + K2 = 0 Solving -25 + -3K + K2 = 0 Solving for variable 'K'. Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + -3K + 25 + K2 = 0 + 25 Reorder the terms: -25 + 25 + -3K + K2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -3K + K2 = 0 + 25 -3K + K2 = 0 + 25 Combine like terms: 0 + 25 = 25 -3K + K2 = 25 The K term is -3K. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3K + 2.25 + K2 = 25 + 2.25 Reorder the terms: 2.25 + -3K + K2 = 25 + 2.25 Combine like terms: 25 + 2.25 = 27.25 2.25 + -3K + K2 = 27.25 Factor a perfect square on the left side: (K + -1.5)(K + -1.5) = 27.25 Calculate the square root of the right side: 5.220153254 Break this problem into two subproblems by setting (K + -1.5) equal to 5.220153254 and -5.220153254.Subproblem 1
K + -1.5 = 5.220153254 Simplifying K + -1.5 = 5.220153254 Reorder the terms: -1.5 + K = 5.220153254 Solving -1.5 + K = 5.220153254 Solving for variable 'K'. Move all terms containing K to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + K = 5.220153254 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + K = 5.220153254 + 1.5 K = 5.220153254 + 1.5 Combine like terms: 5.220153254 + 1.5 = 6.720153254 K = 6.720153254 Simplifying K = 6.720153254Subproblem 2
K + -1.5 = -5.220153254 Simplifying K + -1.5 = -5.220153254 Reorder the terms: -1.5 + K = -5.220153254 Solving -1.5 + K = -5.220153254 Solving for variable 'K'. Move all terms containing K to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + K = -5.220153254 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + K = -5.220153254 + 1.5 K = -5.220153254 + 1.5 Combine like terms: -5.220153254 + 1.5 = -3.720153254 K = -3.720153254 Simplifying K = -3.720153254Solution
The solution to the problem is based on the solutions from the subproblems. K = {6.720153254, -3.720153254}
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