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Simplifying k2 + -27k + 22 = 0 Reorder the terms: 22 + -27k + k2 = 0 Solving 22 + -27k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '-22' to each side of the equation. 22 + -27k + -22 + k2 = 0 + -22 Reorder the terms: 22 + -22 + -27k + k2 = 0 + -22 Combine like terms: 22 + -22 = 0 0 + -27k + k2 = 0 + -22 -27k + k2 = 0 + -22 Combine like terms: 0 + -22 = -22 -27k + k2 = -22 The k term is -27k. Take half its coefficient (-13.5). Square it (182.25) and add it to both sides. Add '182.25' to each side of the equation. -27k + 182.25 + k2 = -22 + 182.25 Reorder the terms: 182.25 + -27k + k2 = -22 + 182.25 Combine like terms: -22 + 182.25 = 160.25 182.25 + -27k + k2 = 160.25 Factor a perfect square on the left side: (k + -13.5)(k + -13.5) = 160.25 Calculate the square root of the right side: 12.658988901 Break this problem into two subproblems by setting (k + -13.5) equal to 12.658988901 and -12.658988901.Subproblem 1
k + -13.5 = 12.658988901 Simplifying k + -13.5 = 12.658988901 Reorder the terms: -13.5 + k = 12.658988901 Solving -13.5 + k = 12.658988901 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + k = 12.658988901 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + k = 12.658988901 + 13.5 k = 12.658988901 + 13.5 Combine like terms: 12.658988901 + 13.5 = 26.158988901 k = 26.158988901 Simplifying k = 26.158988901Subproblem 2
k + -13.5 = -12.658988901 Simplifying k + -13.5 = -12.658988901 Reorder the terms: -13.5 + k = -12.658988901 Solving -13.5 + k = -12.658988901 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + k = -12.658988901 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + k = -12.658988901 + 13.5 k = -12.658988901 + 13.5 Combine like terms: -12.658988901 + 13.5 = 0.841011099 k = 0.841011099 Simplifying k = 0.841011099Solution
The solution to the problem is based on the solutions from the subproblems. k = {26.158988901, 0.841011099}
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