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Simplifying k2 + -11k + -20 = 0 Reorder the terms: -20 + -11k + k2 = 0 Solving -20 + -11k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + -11k + 20 + k2 = 0 + 20 Reorder the terms: -20 + 20 + -11k + k2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -11k + k2 = 0 + 20 -11k + k2 = 0 + 20 Combine like terms: 0 + 20 = 20 -11k + k2 = 20 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 = 20 + 30.25 Reorder the terms: 30.25 + -11k + k2 = 20 + 30.25 Combine like terms: 20 + 30.25 = 50.25 30.25 + -11k + k2 = 50.25 Factor a perfect square on the left side: (k + -5.5)(k + -5.5) = 50.25 Calculate the square root of the right side: 7.088723439 Break this problem into two subproblems by setting (k + -5.5) equal to 7.088723439 and -7.088723439.Subproblem 1
k + -5.5 = 7.088723439 Simplifying k + -5.5 = 7.088723439 Reorder the terms: -5.5 + k = 7.088723439 Solving -5.5 + k = 7.088723439 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 = 7.088723439 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + k = 7.088723439 + 5.5 k = 7.088723439 + 5.5 Combine like terms: 7.088723439 + 5.5 = 12.588723439 k = 12.588723439 Simplifying k = 12.588723439Subproblem 2
k + -5.5 = -7.088723439 Simplifying k + -5.5 = -7.088723439 Reorder the terms: -5.5 + k = -7.088723439 Solving -5.5 + k = -7.088723439 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 = -7.088723439 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + k = -7.088723439 + 5.5 k = -7.088723439 + 5.5 Combine like terms: -7.088723439 + 5.5 = -1.588723439 k = -1.588723439 Simplifying k = -1.588723439Solution
The solution to the problem is based on the solutions from the subproblems. k = {12.588723439, -1.588723439}
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