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Simplifying k2 + 6k + -81 = 0 Reorder the terms: -81 + 6k + k2 = 0 Solving -81 + 6k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '81' to each side of the equation. -81 + 6k + 81 + k2 = 0 + 81 Reorder the terms: -81 + 81 + 6k + k2 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + 6k + k2 = 0 + 81 6k + k2 = 0 + 81 Combine like terms: 0 + 81 = 81 6k + k2 = 81 The k term is 6k. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6k + 9 + k2 = 81 + 9 Reorder the terms: 9 + 6k + k2 = 81 + 9 Combine like terms: 81 + 9 = 90 9 + 6k + k2 = 90 Factor a perfect square on the left side: (k + 3)(k + 3) = 90 Calculate the square root of the right side: 9.486832981 Break this problem into two subproblems by setting (k + 3) equal to 9.486832981 and -9.486832981.Subproblem 1
k + 3 = 9.486832981 Simplifying k + 3 = 9.486832981 Reorder the terms: 3 + k = 9.486832981 Solving 3 + k = 9.486832981 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + k = 9.486832981 + -3 Combine like terms: 3 + -3 = 0 0 + k = 9.486832981 + -3 k = 9.486832981 + -3 Combine like terms: 9.486832981 + -3 = 6.486832981 k = 6.486832981 Simplifying k = 6.486832981Subproblem 2
k + 3 = -9.486832981 Simplifying k + 3 = -9.486832981 Reorder the terms: 3 + k = -9.486832981 Solving 3 + k = -9.486832981 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + k = -9.486832981 + -3 Combine like terms: 3 + -3 = 0 0 + k = -9.486832981 + -3 k = -9.486832981 + -3 Combine like terms: -9.486832981 + -3 = -12.486832981 k = -12.486832981 Simplifying k = -12.486832981Solution
The solution to the problem is based on the solutions from the subproblems. k = {6.486832981, -12.486832981}
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