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Simplifying n2 + 4n + -8 = 0 Reorder the terms: -8 + 4n + n2 = 0 Solving -8 + 4n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 4n + 8 + n2 = 0 + 8 Reorder the terms: -8 + 8 + 4n + n2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 4n + n2 = 0 + 8 4n + n2 = 0 + 8 Combine like terms: 0 + 8 = 8 4n + n2 = 8 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 = 8 + 4 Reorder the terms: 4 + 4n + n2 = 8 + 4 Combine like terms: 8 + 4 = 12 4 + 4n + n2 = 12 Factor a perfect square on the left side: (n + 2)(n + 2) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (n + 2) equal to 3.464101615 and -3.464101615.Subproblem 1
n + 2 = 3.464101615 Simplifying n + 2 = 3.464101615 Reorder the terms: 2 + n = 3.464101615 Solving 2 + n = 3.464101615 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 = 3.464101615 + -2 Combine like terms: 2 + -2 = 0 0 + n = 3.464101615 + -2 n = 3.464101615 + -2 Combine like terms: 3.464101615 + -2 = 1.464101615 n = 1.464101615 Simplifying n = 1.464101615Subproblem 2
n + 2 = -3.464101615 Simplifying n + 2 = -3.464101615 Reorder the terms: 2 + n = -3.464101615 Solving 2 + n = -3.464101615 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 = -3.464101615 + -2 Combine like terms: 2 + -2 = 0 0 + n = -3.464101615 + -2 n = -3.464101615 + -2 Combine like terms: -3.464101615 + -2 = -5.464101615 n = -5.464101615 Simplifying n = -5.464101615Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.464101615, -5.464101615}
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