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Simplifying k2 + 11k = 14 Reorder the terms: 11k + k2 = 14 Solving 11k + k2 = 14 Solving for variable 'k'. Reorder the terms: -14 + 11k + k2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + 11k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + 11k + 14 + k2 = 0 + 14 Reorder the terms: -14 + 14 + 11k + k2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 11k + k2 = 0 + 14 11k + k2 = 0 + 14 Combine like terms: 0 + 14 = 14 11k + k2 = 14 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 = 14 + 30.25 Reorder the terms: 30.25 + 11k + k2 = 14 + 30.25 Combine like terms: 14 + 30.25 = 44.25 30.25 + 11k + k2 = 44.25 Factor a perfect square on the left side: (k + 5.5)(k + 5.5) = 44.25 Calculate the square root of the right side: 6.652067348 Break this problem into two subproblems by setting (k + 5.5) equal to 6.652067348 and -6.652067348.Subproblem 1
k + 5.5 = 6.652067348 Simplifying k + 5.5 = 6.652067348 Reorder the terms: 5.5 + k = 6.652067348 Solving 5.5 + k = 6.652067348 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 = 6.652067348 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + k = 6.652067348 + -5.5 k = 6.652067348 + -5.5 Combine like terms: 6.652067348 + -5.5 = 1.152067348 k = 1.152067348 Simplifying k = 1.152067348Subproblem 2
k + 5.5 = -6.652067348 Simplifying k + 5.5 = -6.652067348 Reorder the terms: 5.5 + k = -6.652067348 Solving 5.5 + k = -6.652067348 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 = -6.652067348 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + k = -6.652067348 + -5.5 k = -6.652067348 + -5.5 Combine like terms: -6.652067348 + -5.5 = -12.152067348 k = -12.152067348 Simplifying k = -12.152067348Solution
The solution to the problem is based on the solutions from the subproblems. k = {1.152067348, -12.152067348}
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