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Simplifying 2k2 + 22k = 60 Reorder the terms: 22k + 2k2 = 60 Solving 22k + 2k2 = 60 Solving for variable 'k'. Reorder the terms: -60 + 22k + 2k2 = 60 + -60 Combine like terms: 60 + -60 = 0 -60 + 22k + 2k2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-30 + 11k + k2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-30 + 11k + k2)' equal to zero and attempt to solve: Simplifying -30 + 11k + k2 = 0 Solving -30 + 11k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + 11k + 30 + k2 = 0 + 30 Reorder the terms: -30 + 30 + 11k + k2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 11k + k2 = 0 + 30 11k + k2 = 0 + 30 Combine like terms: 0 + 30 = 30 11k + k2 = 30 The k term is 11k. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11k + 30.25 + k2 = 30 + 30.25 Reorder the terms: 30.25 + 11k + k2 = 30 + 30.25 Combine like terms: 30 + 30.25 = 60.25 30.25 + 11k + k2 = 60.25 Factor a perfect square on the left side: (k + 5.5)(k + 5.5) = 60.25 Calculate the square root of the right side: 7.762087348 Break this problem into two subproblems by setting (k + 5.5) equal to 7.762087348 and -7.762087348.Subproblem 1
k + 5.5 = 7.762087348 Simplifying k + 5.5 = 7.762087348 Reorder the terms: 5.5 + k = 7.762087348 Solving 5.5 + k = 7.762087348 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + k = 7.762087348 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + k = 7.762087348 + -5.5 k = 7.762087348 + -5.5 Combine like terms: 7.762087348 + -5.5 = 2.262087348 k = 2.262087348 Simplifying k = 2.262087348Subproblem 2
k + 5.5 = -7.762087348 Simplifying k + 5.5 = -7.762087348 Reorder the terms: 5.5 + k = -7.762087348 Solving 5.5 + k = -7.762087348 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + k = -7.762087348 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + k = -7.762087348 + -5.5 k = -7.762087348 + -5.5 Combine like terms: -7.762087348 + -5.5 = -13.262087348 k = -13.262087348 Simplifying k = -13.262087348Solution
The solution to the problem is based on the solutions from the subproblems. k = {2.262087348, -13.262087348}Solution
k = {2.262087348, -13.262087348}
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