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Simplifying k2 + -18k + -23 = 0 Reorder the terms: -23 + -18k + k2 = 0 Solving -23 + -18k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + -18k + 23 + k2 = 0 + 23 Reorder the terms: -23 + 23 + -18k + k2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -18k + k2 = 0 + 23 -18k + k2 = 0 + 23 Combine like terms: 0 + 23 = 23 -18k + k2 = 23 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 = 23 + 81 Reorder the terms: 81 + -18k + k2 = 23 + 81 Combine like terms: 23 + 81 = 104 81 + -18k + k2 = 104 Factor a perfect square on the left side: (k + -9)(k + -9) = 104 Calculate the square root of the right side: 10.198039027 Break this problem into two subproblems by setting (k + -9) equal to 10.198039027 and -10.198039027.Subproblem 1
k + -9 = 10.198039027 Simplifying k + -9 = 10.198039027 Reorder the terms: -9 + k = 10.198039027 Solving -9 + k = 10.198039027 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 = 10.198039027 + 9 Combine like terms: -9 + 9 = 0 0 + k = 10.198039027 + 9 k = 10.198039027 + 9 Combine like terms: 10.198039027 + 9 = 19.198039027 k = 19.198039027 Simplifying k = 19.198039027Subproblem 2
k + -9 = -10.198039027 Simplifying k + -9 = -10.198039027 Reorder the terms: -9 + k = -10.198039027 Solving -9 + k = -10.198039027 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 = -10.198039027 + 9 Combine like terms: -9 + 9 = 0 0 + k = -10.198039027 + 9 k = -10.198039027 + 9 Combine like terms: -10.198039027 + 9 = -1.198039027 k = -1.198039027 Simplifying k = -1.198039027Solution
The solution to the problem is based on the solutions from the subproblems. k = {19.198039027, -1.198039027}
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