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Simplifying n2 + 16n + -1 = 0 Reorder the terms: -1 + 16n + n2 = 0 Solving -1 + 16n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 16n + 1 + n2 = 0 + 1 Reorder the terms: -1 + 1 + 16n + n2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 16n + n2 = 0 + 1 16n + n2 = 0 + 1 Combine like terms: 0 + 1 = 1 16n + n2 = 1 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 = 1 + 64 Reorder the terms: 64 + 16n + n2 = 1 + 64 Combine like terms: 1 + 64 = 65 64 + 16n + n2 = 65 Factor a perfect square on the left side: (n + 8)(n + 8) = 65 Calculate the square root of the right side: 8.062257748 Break this problem into two subproblems by setting (n + 8) equal to 8.062257748 and -8.062257748.Subproblem 1
n + 8 = 8.062257748 Simplifying n + 8 = 8.062257748 Reorder the terms: 8 + n = 8.062257748 Solving 8 + n = 8.062257748 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 = 8.062257748 + -8 Combine like terms: 8 + -8 = 0 0 + n = 8.062257748 + -8 n = 8.062257748 + -8 Combine like terms: 8.062257748 + -8 = 0.062257748 n = 0.062257748 Simplifying n = 0.062257748Subproblem 2
n + 8 = -8.062257748 Simplifying n + 8 = -8.062257748 Reorder the terms: 8 + n = -8.062257748 Solving 8 + n = -8.062257748 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 = -8.062257748 + -8 Combine like terms: 8 + -8 = 0 0 + n = -8.062257748 + -8 n = -8.062257748 + -8 Combine like terms: -8.062257748 + -8 = -16.062257748 n = -16.062257748 Simplifying n = -16.062257748Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.062257748, -16.062257748}
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