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Simplifying n2 + 16n + -64 = 0 Reorder the terms: -64 + 16n + n2 = 0 Solving -64 + 16n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + 16n + 64 + n2 = 0 + 64 Reorder the terms: -64 + 64 + 16n + n2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 16n + n2 = 0 + 64 16n + n2 = 0 + 64 Combine like terms: 0 + 64 = 64 16n + n2 = 64 The n term is 16n. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16n + 64 + n2 = 64 + 64 Reorder the terms: 64 + 16n + n2 = 64 + 64 Combine like terms: 64 + 64 = 128 64 + 16n + n2 = 128 Factor a perfect square on the left side: (n + 8)(n + 8) = 128 Calculate the square root of the right side: 11.313708499 Break this problem into two subproblems by setting (n + 8) equal to 11.313708499 and -11.313708499.Subproblem 1
n + 8 = 11.313708499 Simplifying n + 8 = 11.313708499 Reorder the terms: 8 + n = 11.313708499 Solving 8 + n = 11.313708499 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + n = 11.313708499 + -8 Combine like terms: 8 + -8 = 0 0 + n = 11.313708499 + -8 n = 11.313708499 + -8 Combine like terms: 11.313708499 + -8 = 3.313708499 n = 3.313708499 Simplifying n = 3.313708499Subproblem 2
n + 8 = -11.313708499 Simplifying n + 8 = -11.313708499 Reorder the terms: 8 + n = -11.313708499 Solving 8 + n = -11.313708499 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + n = -11.313708499 + -8 Combine like terms: 8 + -8 = 0 0 + n = -11.313708499 + -8 n = -11.313708499 + -8 Combine like terms: -11.313708499 + -8 = -19.313708499 n = -19.313708499 Simplifying n = -19.313708499Solution
The solution to the problem is based on the solutions from the subproblems. n = {3.313708499, -19.313708499}
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