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Simplifying k2 + -18k + 18 = 0 Reorder the terms: 18 + -18k + k2 = 0 Solving 18 + -18k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + -18k + -18 + k2 = 0 + -18 Reorder the terms: 18 + -18 + -18k + k2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -18k + k2 = 0 + -18 -18k + k2 = 0 + -18 Combine like terms: 0 + -18 = -18 -18k + k2 = -18 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 = -18 + 81 Reorder the terms: 81 + -18k + k2 = -18 + 81 Combine like terms: -18 + 81 = 63 81 + -18k + k2 = 63 Factor a perfect square on the left side: (k + -9)(k + -9) = 63 Calculate the square root of the right side: 7.937253933 Break this problem into two subproblems by setting (k + -9) equal to 7.937253933 and -7.937253933.Subproblem 1
k + -9 = 7.937253933 Simplifying k + -9 = 7.937253933 Reorder the terms: -9 + k = 7.937253933 Solving -9 + k = 7.937253933 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 = 7.937253933 + 9 Combine like terms: -9 + 9 = 0 0 + k = 7.937253933 + 9 k = 7.937253933 + 9 Combine like terms: 7.937253933 + 9 = 16.937253933 k = 16.937253933 Simplifying k = 16.937253933Subproblem 2
k + -9 = -7.937253933 Simplifying k + -9 = -7.937253933 Reorder the terms: -9 + k = -7.937253933 Solving -9 + k = -7.937253933 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 = -7.937253933 + 9 Combine like terms: -9 + 9 = 0 0 + k = -7.937253933 + 9 k = -7.937253933 + 9 Combine like terms: -7.937253933 + 9 = 1.062746067 k = 1.062746067 Simplifying k = 1.062746067Solution
The solution to the problem is based on the solutions from the subproblems. k = {16.937253933, 1.062746067}
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