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Simplifying n2 + 4n + -160 = 0 Reorder the terms: -160 + 4n + n2 = 0 Solving -160 + 4n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '160' to each side of the equation. -160 + 4n + 160 + n2 = 0 + 160 Reorder the terms: -160 + 160 + 4n + n2 = 0 + 160 Combine like terms: -160 + 160 = 0 0 + 4n + n2 = 0 + 160 4n + n2 = 0 + 160 Combine like terms: 0 + 160 = 160 4n + n2 = 160 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 = 160 + 4 Reorder the terms: 4 + 4n + n2 = 160 + 4 Combine like terms: 160 + 4 = 164 4 + 4n + n2 = 164 Factor a perfect square on the left side: (n + 2)(n + 2) = 164 Calculate the square root of the right side: 12.806248475 Break this problem into two subproblems by setting (n + 2) equal to 12.806248475 and -12.806248475.Subproblem 1
n + 2 = 12.806248475 Simplifying n + 2 = 12.806248475 Reorder the terms: 2 + n = 12.806248475 Solving 2 + n = 12.806248475 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 = 12.806248475 + -2 Combine like terms: 2 + -2 = 0 0 + n = 12.806248475 + -2 n = 12.806248475 + -2 Combine like terms: 12.806248475 + -2 = 10.806248475 n = 10.806248475 Simplifying n = 10.806248475Subproblem 2
n + 2 = -12.806248475 Simplifying n + 2 = -12.806248475 Reorder the terms: 2 + n = -12.806248475 Solving 2 + n = -12.806248475 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 = -12.806248475 + -2 Combine like terms: 2 + -2 = 0 0 + n = -12.806248475 + -2 n = -12.806248475 + -2 Combine like terms: -12.806248475 + -2 = -14.806248475 n = -14.806248475 Simplifying n = -14.806248475Solution
The solution to the problem is based on the solutions from the subproblems. n = {10.806248475, -14.806248475}
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