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Simplifying k2 + 8k + -24 = 0 Reorder the terms: -24 + 8k + k2 = 0 Solving -24 + 8k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + 8k + 24 + k2 = 0 + 24 Reorder the terms: -24 + 24 + 8k + k2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 8k + k2 = 0 + 24 8k + k2 = 0 + 24 Combine like terms: 0 + 24 = 24 8k + k2 = 24 The k term is 8k. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8k + 16 + k2 = 24 + 16 Reorder the terms: 16 + 8k + k2 = 24 + 16 Combine like terms: 24 + 16 = 40 16 + 8k + k2 = 40 Factor a perfect square on the left side: (k + 4)(k + 4) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (k + 4) equal to 6.32455532 and -6.32455532.Subproblem 1
k + 4 = 6.32455532 Simplifying k + 4 = 6.32455532 Reorder the terms: 4 + k = 6.32455532 Solving 4 + k = 6.32455532 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + k = 6.32455532 + -4 Combine like terms: 4 + -4 = 0 0 + k = 6.32455532 + -4 k = 6.32455532 + -4 Combine like terms: 6.32455532 + -4 = 2.32455532 k = 2.32455532 Simplifying k = 2.32455532Subproblem 2
k + 4 = -6.32455532 Simplifying k + 4 = -6.32455532 Reorder the terms: 4 + k = -6.32455532 Solving 4 + k = -6.32455532 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + k = -6.32455532 + -4 Combine like terms: 4 + -4 = 0 0 + k = -6.32455532 + -4 k = -6.32455532 + -4 Combine like terms: -6.32455532 + -4 = -10.32455532 k = -10.32455532 Simplifying k = -10.32455532Solution
The solution to the problem is based on the solutions from the subproblems. k = {2.32455532, -10.32455532}
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