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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 = 3.414213562 n = 3.414213562 Simplifying n = 3.414213562Subproblem 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 = 0.585786438 n = 0.585786438 Simplifying n = 0.585786438Solution
The solution to the problem is based on the solutions from the subproblems. n = {3.414213562, 0.585786438}
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