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Simplifying K2 + 10K = 575 Reorder the terms: 10K + K2 = 575 Solving 10K + K2 = 575 Solving for variable 'K'. Reorder the terms: -575 + 10K + K2 = 575 + -575 Combine like terms: 575 + -575 = 0 -575 + 10K + K2 = 0 Begin completing the square. Move the constant term to the right: Add '575' to each side of the equation. -575 + 10K + 575 + K2 = 0 + 575 Reorder the terms: -575 + 575 + 10K + K2 = 0 + 575 Combine like terms: -575 + 575 = 0 0 + 10K + K2 = 0 + 575 10K + K2 = 0 + 575 Combine like terms: 0 + 575 = 575 10K + K2 = 575 The K term is 10K. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10K + 25 + K2 = 575 + 25 Reorder the terms: 25 + 10K + K2 = 575 + 25 Combine like terms: 575 + 25 = 600 25 + 10K + K2 = 600 Factor a perfect square on the left side: (K + 5)(K + 5) = 600 Calculate the square root of the right side: 24.494897428 Break this problem into two subproblems by setting (K + 5) equal to 24.494897428 and -24.494897428.Subproblem 1
K + 5 = 24.494897428 Simplifying K + 5 = 24.494897428 Reorder the terms: 5 + K = 24.494897428 Solving 5 + K = 24.494897428 Solving for variable 'K'. Move all terms containing K to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + K = 24.494897428 + -5 Combine like terms: 5 + -5 = 0 0 + K = 24.494897428 + -5 K = 24.494897428 + -5 Combine like terms: 24.494897428 + -5 = 19.494897428 K = 19.494897428 Simplifying K = 19.494897428Subproblem 2
K + 5 = -24.494897428 Simplifying K + 5 = -24.494897428 Reorder the terms: 5 + K = -24.494897428 Solving 5 + K = -24.494897428 Solving for variable 'K'. Move all terms containing K to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + K = -24.494897428 + -5 Combine like terms: 5 + -5 = 0 0 + K = -24.494897428 + -5 K = -24.494897428 + -5 Combine like terms: -24.494897428 + -5 = -29.494897428 K = -29.494897428 Simplifying K = -29.494897428Solution
The solution to the problem is based on the solutions from the subproblems. K = {19.494897428, -29.494897428}
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