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Simplifying n2 + 16n + 6 = 0 Reorder the terms: 6 + 16n + n2 = 0 Solving 6 + 16n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + 16n + -6 + n2 = 0 + -6 Reorder the terms: 6 + -6 + 16n + n2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 16n + n2 = 0 + -6 16n + n2 = 0 + -6 Combine like terms: 0 + -6 = -6 16n + n2 = -6 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 = -6 + 64 Reorder the terms: 64 + 16n + n2 = -6 + 64 Combine like terms: -6 + 64 = 58 64 + 16n + n2 = 58 Factor a perfect square on the left side: (n + 8)(n + 8) = 58 Calculate the square root of the right side: 7.615773106 Break this problem into two subproblems by setting (n + 8) equal to 7.615773106 and -7.615773106.Subproblem 1
n + 8 = 7.615773106 Simplifying n + 8 = 7.615773106 Reorder the terms: 8 + n = 7.615773106 Solving 8 + n = 7.615773106 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 = 7.615773106 + -8 Combine like terms: 8 + -8 = 0 0 + n = 7.615773106 + -8 n = 7.615773106 + -8 Combine like terms: 7.615773106 + -8 = -0.384226894 n = -0.384226894 Simplifying n = -0.384226894Subproblem 2
n + 8 = -7.615773106 Simplifying n + 8 = -7.615773106 Reorder the terms: 8 + n = -7.615773106 Solving 8 + n = -7.615773106 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 = -7.615773106 + -8 Combine like terms: 8 + -8 = 0 0 + n = -7.615773106 + -8 n = -7.615773106 + -8 Combine like terms: -7.615773106 + -8 = -15.615773106 n = -15.615773106 Simplifying n = -15.615773106Solution
The solution to the problem is based on the solutions from the subproblems. n = {-0.384226894, -15.615773106}
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