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Simplifying k2 + -4 = -8k Reorder the terms: -4 + k2 = -8k Solving -4 + k2 = -8k Solving for variable 'k'. Reorder the terms: -4 + 8k + k2 = -8k + 8k Combine like terms: -8k + 8k = 0 -4 + 8k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 8k + 4 + k2 = 0 + 4 Reorder the terms: -4 + 4 + 8k + k2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 8k + k2 = 0 + 4 8k + k2 = 0 + 4 Combine like terms: 0 + 4 = 4 8k + k2 = 4 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 = 4 + 16 Reorder the terms: 16 + 8k + k2 = 4 + 16 Combine like terms: 4 + 16 = 20 16 + 8k + k2 = 20 Factor a perfect square on the left side: (k + 4)(k + 4) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (k + 4) equal to 4.472135955 and -4.472135955.Subproblem 1
k + 4 = 4.472135955 Simplifying k + 4 = 4.472135955 Reorder the terms: 4 + k = 4.472135955 Solving 4 + k = 4.472135955 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 = 4.472135955 + -4 Combine like terms: 4 + -4 = 0 0 + k = 4.472135955 + -4 k = 4.472135955 + -4 Combine like terms: 4.472135955 + -4 = 0.472135955 k = 0.472135955 Simplifying k = 0.472135955Subproblem 2
k + 4 = -4.472135955 Simplifying k + 4 = -4.472135955 Reorder the terms: 4 + k = -4.472135955 Solving 4 + k = -4.472135955 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 = -4.472135955 + -4 Combine like terms: 4 + -4 = 0 0 + k = -4.472135955 + -4 k = -4.472135955 + -4 Combine like terms: -4.472135955 + -4 = -8.472135955 k = -8.472135955 Simplifying k = -8.472135955Solution
The solution to the problem is based on the solutions from the subproblems. k = {0.472135955, -8.472135955}
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