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Simplifying n2 + 4n + 2 = 0 Reorder the terms: 2 + 4n + n2 = 0 Solving 2 + 4n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 4n + -2 + n2 = 0 + -2 Reorder the terms: 2 + -2 + 4n + n2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 4n + n2 = 0 + -2 4n + n2 = 0 + -2 Combine like terms: 0 + -2 = -2 4n + n2 = -2 The n term is 4n. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4n + 4 + n2 = -2 + 4 Reorder the terms: 4 + 4n + n2 = -2 + 4 Combine like terms: -2 + 4 = 2 4 + 4n + n2 = 2 Factor a perfect square on the left side: (n + 2)(n + 2) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (n + 2) equal to 1.414213562 and -1.414213562.Subproblem 1
n + 2 = 1.414213562 Simplifying n + 2 = 1.414213562 Reorder the terms: 2 + n = 1.414213562 Solving 2 + n = 1.414213562 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + n = 1.414213562 + -2 Combine like terms: 2 + -2 = 0 0 + n = 1.414213562 + -2 n = 1.414213562 + -2 Combine like terms: 1.414213562 + -2 = -0.585786438 n = -0.585786438 Simplifying n = -0.585786438Subproblem 2
n + 2 = -1.414213562 Simplifying n + 2 = -1.414213562 Reorder the terms: 2 + n = -1.414213562 Solving 2 + n = -1.414213562 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + n = -1.414213562 + -2 Combine like terms: 2 + -2 = 0 0 + n = -1.414213562 + -2 n = -1.414213562 + -2 Combine like terms: -1.414213562 + -2 = -3.414213562 n = -3.414213562 Simplifying n = -3.414213562Solution
The solution to the problem is based on the solutions from the subproblems. n = {-0.585786438, -3.414213562}
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