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Simplifying k2 + -200k + 6000 = 0 Reorder the terms: 6000 + -200k + k2 = 0 Solving 6000 + -200k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '-6000' to each side of the equation. 6000 + -200k + -6000 + k2 = 0 + -6000 Reorder the terms: 6000 + -6000 + -200k + k2 = 0 + -6000 Combine like terms: 6000 + -6000 = 0 0 + -200k + k2 = 0 + -6000 -200k + k2 = 0 + -6000 Combine like terms: 0 + -6000 = -6000 -200k + k2 = -6000 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 = -6000 + 10000 Reorder the terms: 10000 + -200k + k2 = -6000 + 10000 Combine like terms: -6000 + 10000 = 4000 10000 + -200k + k2 = 4000 Factor a perfect square on the left side: (k + -100)(k + -100) = 4000 Calculate the square root of the right side: 63.245553203 Break this problem into two subproblems by setting (k + -100) equal to 63.245553203 and -63.245553203.Subproblem 1
k + -100 = 63.245553203 Simplifying k + -100 = 63.245553203 Reorder the terms: -100 + k = 63.245553203 Solving -100 + k = 63.245553203 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 = 63.245553203 + 100 Combine like terms: -100 + 100 = 0 0 + k = 63.245553203 + 100 k = 63.245553203 + 100 Combine like terms: 63.245553203 + 100 = 163.245553203 k = 163.245553203 Simplifying k = 163.245553203Subproblem 2
k + -100 = -63.245553203 Simplifying k + -100 = -63.245553203 Reorder the terms: -100 + k = -63.245553203 Solving -100 + k = -63.245553203 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 = -63.245553203 + 100 Combine like terms: -100 + 100 = 0 0 + k = -63.245553203 + 100 k = -63.245553203 + 100 Combine like terms: -63.245553203 + 100 = 36.754446797 k = 36.754446797 Simplifying k = 36.754446797Solution
The solution to the problem is based on the solutions from the subproblems. k = {163.245553203, 36.754446797}
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