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Simplifying k2 + -200k + 600 = 0 Reorder the terms: 600 + -200k + k2 = 0 Solving 600 + -200k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '-600' to each side of the equation. 600 + -200k + -600 + k2 = 0 + -600 Reorder the terms: 600 + -600 + -200k + k2 = 0 + -600 Combine like terms: 600 + -600 = 0 0 + -200k + k2 = 0 + -600 -200k + k2 = 0 + -600 Combine like terms: 0 + -600 = -600 -200k + k2 = -600 The k term is -200k. Take half its coefficient (-100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. -200k + 10000 + k2 = -600 + 10000 Reorder the terms: 10000 + -200k + k2 = -600 + 10000 Combine like terms: -600 + 10000 = 9400 10000 + -200k + k2 = 9400 Factor a perfect square on the left side: (k + -100)(k + -100) = 9400 Calculate the square root of the right side: 96.953597148 Break this problem into two subproblems by setting (k + -100) equal to 96.953597148 and -96.953597148.Subproblem 1
k + -100 = 96.953597148 Simplifying k + -100 = 96.953597148 Reorder the terms: -100 + k = 96.953597148 Solving -100 + k = 96.953597148 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + k = 96.953597148 + 100 Combine like terms: -100 + 100 = 0 0 + k = 96.953597148 + 100 k = 96.953597148 + 100 Combine like terms: 96.953597148 + 100 = 196.953597148 k = 196.953597148 Simplifying k = 196.953597148Subproblem 2
k + -100 = -96.953597148 Simplifying k + -100 = -96.953597148 Reorder the terms: -100 + k = -96.953597148 Solving -100 + k = -96.953597148 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + k = -96.953597148 + 100 Combine like terms: -100 + 100 = 0 0 + k = -96.953597148 + 100 k = -96.953597148 + 100 Combine like terms: -96.953597148 + 100 = 3.046402852 k = 3.046402852 Simplifying k = 3.046402852Solution
The solution to the problem is based on the solutions from the subproblems. k = {196.953597148, 3.046402852}
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