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Simplifying k2 + 18k + -42 = 0 Reorder the terms: -42 + 18k + k2 = 0 Solving -42 + 18k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + 18k + 42 + k2 = 0 + 42 Reorder the terms: -42 + 42 + 18k + k2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + 18k + k2 = 0 + 42 18k + k2 = 0 + 42 Combine like terms: 0 + 42 = 42 18k + k2 = 42 The k term is 18k. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18k + 81 + k2 = 42 + 81 Reorder the terms: 81 + 18k + k2 = 42 + 81 Combine like terms: 42 + 81 = 123 81 + 18k + k2 = 123 Factor a perfect square on the left side: (k + 9)(k + 9) = 123 Calculate the square root of the right side: 11.090536506 Break this problem into two subproblems by setting (k + 9) equal to 11.090536506 and -11.090536506.Subproblem 1
k + 9 = 11.090536506 Simplifying k + 9 = 11.090536506 Reorder the terms: 9 + k = 11.090536506 Solving 9 + k = 11.090536506 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + k = 11.090536506 + -9 Combine like terms: 9 + -9 = 0 0 + k = 11.090536506 + -9 k = 11.090536506 + -9 Combine like terms: 11.090536506 + -9 = 2.090536506 k = 2.090536506 Simplifying k = 2.090536506Subproblem 2
k + 9 = -11.090536506 Simplifying k + 9 = -11.090536506 Reorder the terms: 9 + k = -11.090536506 Solving 9 + k = -11.090536506 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + k = -11.090536506 + -9 Combine like terms: 9 + -9 = 0 0 + k = -11.090536506 + -9 k = -11.090536506 + -9 Combine like terms: -11.090536506 + -9 = -20.090536506 k = -20.090536506 Simplifying k = -20.090536506Solution
The solution to the problem is based on the solutions from the subproblems. k = {2.090536506, -20.090536506}
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