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Simplifying n2 + 16n + -89 = 0 Reorder the terms: -89 + 16n + n2 = 0 Solving -89 + 16n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '89' to each side of the equation. -89 + 16n + 89 + n2 = 0 + 89 Reorder the terms: -89 + 89 + 16n + n2 = 0 + 89 Combine like terms: -89 + 89 = 0 0 + 16n + n2 = 0 + 89 16n + n2 = 0 + 89 Combine like terms: 0 + 89 = 89 16n + n2 = 89 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 = 89 + 64 Reorder the terms: 64 + 16n + n2 = 89 + 64 Combine like terms: 89 + 64 = 153 64 + 16n + n2 = 153 Factor a perfect square on the left side: (n + 8)(n + 8) = 153 Calculate the square root of the right side: 12.369316877 Break this problem into two subproblems by setting (n + 8) equal to 12.369316877 and -12.369316877.Subproblem 1
n + 8 = 12.369316877 Simplifying n + 8 = 12.369316877 Reorder the terms: 8 + n = 12.369316877 Solving 8 + n = 12.369316877 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 = 12.369316877 + -8 Combine like terms: 8 + -8 = 0 0 + n = 12.369316877 + -8 n = 12.369316877 + -8 Combine like terms: 12.369316877 + -8 = 4.369316877 n = 4.369316877 Simplifying n = 4.369316877Subproblem 2
n + 8 = -12.369316877 Simplifying n + 8 = -12.369316877 Reorder the terms: 8 + n = -12.369316877 Solving 8 + n = -12.369316877 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 = -12.369316877 + -8 Combine like terms: 8 + -8 = 0 0 + n = -12.369316877 + -8 n = -12.369316877 + -8 Combine like terms: -12.369316877 + -8 = -20.369316877 n = -20.369316877 Simplifying n = -20.369316877Solution
The solution to the problem is based on the solutions from the subproblems. n = {4.369316877, -20.369316877}
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