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Simplifying k2 + 72 = 33k Reorder the terms: 72 + k2 = 33k Solving 72 + k2 = 33k Solving for variable 'k'. Reorder the terms: 72 + -33k + k2 = 33k + -33k Combine like terms: 33k + -33k = 0 72 + -33k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '-72' to each side of the equation. 72 + -33k + -72 + k2 = 0 + -72 Reorder the terms: 72 + -72 + -33k + k2 = 0 + -72 Combine like terms: 72 + -72 = 0 0 + -33k + k2 = 0 + -72 -33k + k2 = 0 + -72 Combine like terms: 0 + -72 = -72 -33k + k2 = -72 The k term is -33k. Take half its coefficient (-16.5). Square it (272.25) and add it to both sides. Add '272.25' to each side of the equation. -33k + 272.25 + k2 = -72 + 272.25 Reorder the terms: 272.25 + -33k + k2 = -72 + 272.25 Combine like terms: -72 + 272.25 = 200.25 272.25 + -33k + k2 = 200.25 Factor a perfect square on the left side: (k + -16.5)(k + -16.5) = 200.25 Calculate the square root of the right side: 14.150971698 Break this problem into two subproblems by setting (k + -16.5) equal to 14.150971698 and -14.150971698.Subproblem 1
k + -16.5 = 14.150971698 Simplifying k + -16.5 = 14.150971698 Reorder the terms: -16.5 + k = 14.150971698 Solving -16.5 + k = 14.150971698 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '16.5' to each side of the equation. -16.5 + 16.5 + k = 14.150971698 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + k = 14.150971698 + 16.5 k = 14.150971698 + 16.5 Combine like terms: 14.150971698 + 16.5 = 30.650971698 k = 30.650971698 Simplifying k = 30.650971698Subproblem 2
k + -16.5 = -14.150971698 Simplifying k + -16.5 = -14.150971698 Reorder the terms: -16.5 + k = -14.150971698 Solving -16.5 + k = -14.150971698 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '16.5' to each side of the equation. -16.5 + 16.5 + k = -14.150971698 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + k = -14.150971698 + 16.5 k = -14.150971698 + 16.5 Combine like terms: -14.150971698 + 16.5 = 2.349028302 k = 2.349028302 Simplifying k = 2.349028302Solution
The solution to the problem is based on the solutions from the subproblems. k = {30.650971698, 2.349028302}
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