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Simplifying k2 + 4k + 2 = 0 Reorder the terms: 2 + 4k + k2 = 0 Solving 2 + 4k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 4k + -2 + k2 = 0 + -2 Reorder the terms: 2 + -2 + 4k + k2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 4k + k2 = 0 + -2 4k + k2 = 0 + -2 Combine like terms: 0 + -2 = -2 4k + k2 = -2 The k term is 4k. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4k + 4 + k2 = -2 + 4 Reorder the terms: 4 + 4k + k2 = -2 + 4 Combine like terms: -2 + 4 = 2 4 + 4k + k2 = 2 Factor a perfect square on the left side: (k + 2)(k + 2) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (k + 2) equal to 1.414213562 and -1.414213562.Subproblem 1
k + 2 = 1.414213562 Simplifying k + 2 = 1.414213562 Reorder the terms: 2 + k = 1.414213562 Solving 2 + k = 1.414213562 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + k = 1.414213562 + -2 Combine like terms: 2 + -2 = 0 0 + k = 1.414213562 + -2 k = 1.414213562 + -2 Combine like terms: 1.414213562 + -2 = -0.585786438 k = -0.585786438 Simplifying k = -0.585786438Subproblem 2
k + 2 = -1.414213562 Simplifying k + 2 = -1.414213562 Reorder the terms: 2 + k = -1.414213562 Solving 2 + k = -1.414213562 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + k = -1.414213562 + -2 Combine like terms: 2 + -2 = 0 0 + k = -1.414213562 + -2 k = -1.414213562 + -2 Combine like terms: -1.414213562 + -2 = -3.414213562 k = -3.414213562 Simplifying k = -3.414213562Solution
The solution to the problem is based on the solutions from the subproblems. k = {-0.585786438, -3.414213562}
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