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Simplifying 2n2 + -4n + -2 = 0 Reorder the terms: -2 + -4n + 2n2 = 0 Solving -2 + -4n + 2n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -2n + n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -2n + n2)' equal to zero and attempt to solve: Simplifying -1 + -2n + n2 = 0 Solving -1 + -2n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -2n + 1 + n2 = 0 + 1 Reorder the terms: -1 + 1 + -2n + n2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2n + n2 = 0 + 1 -2n + n2 = 0 + 1 Combine like terms: 0 + 1 = 1 -2n + n2 = 1 The n term is -2n. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2n + 1 + n2 = 1 + 1 Reorder the terms: 1 + -2n + n2 = 1 + 1 Combine like terms: 1 + 1 = 2 1 + -2n + n2 = 2 Factor a perfect square on the left side: (n + -1)(n + -1) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (n + -1) equal to 1.414213562 and -1.414213562.Subproblem 1
n + -1 = 1.414213562 Simplifying n + -1 = 1.414213562 Reorder the terms: -1 + n = 1.414213562 Solving -1 + n = 1.414213562 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n = 1.414213562 + 1 Combine like terms: -1 + 1 = 0 0 + n = 1.414213562 + 1 n = 1.414213562 + 1 Combine like terms: 1.414213562 + 1 = 2.414213562 n = 2.414213562 Simplifying n = 2.414213562Subproblem 2
n + -1 = -1.414213562 Simplifying n + -1 = -1.414213562 Reorder the terms: -1 + n = -1.414213562 Solving -1 + n = -1.414213562 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n = -1.414213562 + 1 Combine like terms: -1 + 1 = 0 0 + n = -1.414213562 + 1 n = -1.414213562 + 1 Combine like terms: -1.414213562 + 1 = -0.414213562 n = -0.414213562 Simplifying n = -0.414213562Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.414213562, -0.414213562}Solution
n = {2.414213562, -0.414213562}
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