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Simplifying k2 + -11k + 14 = 0 Reorder the terms: 14 + -11k + k2 = 0 Solving 14 + -11k + k2 = 0 Solving for variable 'k'. 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 = 16.25 30.25 + -11k + k2 = 16.25 Factor a perfect square on the left side: (k + -5.5)(k + -5.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (k + -5.5) equal to 4.031128874 and -4.031128874.Subproblem 1
k + -5.5 = 4.031128874 Simplifying k + -5.5 = 4.031128874 Reorder the terms: -5.5 + k = 4.031128874 Solving -5.5 + k = 4.031128874 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 = 4.031128874 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + k = 4.031128874 + 5.5 k = 4.031128874 + 5.5 Combine like terms: 4.031128874 + 5.5 = 9.531128874 k = 9.531128874 Simplifying k = 9.531128874Subproblem 2
k + -5.5 = -4.031128874 Simplifying k + -5.5 = -4.031128874 Reorder the terms: -5.5 + k = -4.031128874 Solving -5.5 + k = -4.031128874 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 = -4.031128874 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + k = -4.031128874 + 5.5 k = -4.031128874 + 5.5 Combine like terms: -4.031128874 + 5.5 = 1.468871126 k = 1.468871126 Simplifying k = 1.468871126Solution
The solution to the problem is based on the solutions from the subproblems. k = {9.531128874, 1.468871126}
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