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Simplifying k * k + 18k = -16 Multiply k * k k2 + 18k = -16 Reorder the terms: 18k + k2 = -16 Solving 18k + k2 = -16 Solving for variable 'k'. Reorder the terms: 16 + 18k + k2 = -16 + 16 Combine like terms: -16 + 16 = 0 16 + 18k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + 18k + -16 + k2 = 0 + -16 Reorder the terms: 16 + -16 + 18k + k2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + 18k + k2 = 0 + -16 18k + k2 = 0 + -16 Combine like terms: 0 + -16 = -16 18k + k2 = -16 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 = -16 + 81 Reorder the terms: 81 + 18k + k2 = -16 + 81 Combine like terms: -16 + 81 = 65 81 + 18k + k2 = 65 Factor a perfect square on the left side: (k + 9)(k + 9) = 65 Calculate the square root of the right side: 8.062257748 Break this problem into two subproblems by setting (k + 9) equal to 8.062257748 and -8.062257748.Subproblem 1
k + 9 = 8.062257748 Simplifying k + 9 = 8.062257748 Reorder the terms: 9 + k = 8.062257748 Solving 9 + k = 8.062257748 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 = 8.062257748 + -9 Combine like terms: 9 + -9 = 0 0 + k = 8.062257748 + -9 k = 8.062257748 + -9 Combine like terms: 8.062257748 + -9 = -0.937742252 k = -0.937742252 Simplifying k = -0.937742252Subproblem 2
k + 9 = -8.062257748 Simplifying k + 9 = -8.062257748 Reorder the terms: 9 + k = -8.062257748 Solving 9 + k = -8.062257748 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 = -8.062257748 + -9 Combine like terms: 9 + -9 = 0 0 + k = -8.062257748 + -9 k = -8.062257748 + -9 Combine like terms: -8.062257748 + -9 = -17.062257748 k = -17.062257748 Simplifying k = -17.062257748Solution
The solution to the problem is based on the solutions from the subproblems. k = {-0.937742252, -17.062257748}
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