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Simplifying n2 + 2n + -330 = 0 Reorder the terms: -330 + 2n + n2 = 0 Solving -330 + 2n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '330' to each side of the equation. -330 + 2n + 330 + n2 = 0 + 330 Reorder the terms: -330 + 330 + 2n + n2 = 0 + 330 Combine like terms: -330 + 330 = 0 0 + 2n + n2 = 0 + 330 2n + n2 = 0 + 330 Combine like terms: 0 + 330 = 330 2n + n2 = 330 The n term is 2n. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2n + 1 + n2 = 330 + 1 Reorder the terms: 1 + 2n + n2 = 330 + 1 Combine like terms: 330 + 1 = 331 1 + 2n + n2 = 331 Factor a perfect square on the left side: (n + 1)(n + 1) = 331 Calculate the square root of the right side: 18.193405399 Break this problem into two subproblems by setting (n + 1) equal to 18.193405399 and -18.193405399.Subproblem 1
n + 1 = 18.193405399 Simplifying n + 1 = 18.193405399 Reorder the terms: 1 + n = 18.193405399 Solving 1 + n = 18.193405399 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + n = 18.193405399 + -1 Combine like terms: 1 + -1 = 0 0 + n = 18.193405399 + -1 n = 18.193405399 + -1 Combine like terms: 18.193405399 + -1 = 17.193405399 n = 17.193405399 Simplifying n = 17.193405399Subproblem 2
n + 1 = -18.193405399 Simplifying n + 1 = -18.193405399 Reorder the terms: 1 + n = -18.193405399 Solving 1 + n = -18.193405399 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + n = -18.193405399 + -1 Combine like terms: 1 + -1 = 0 0 + n = -18.193405399 + -1 n = -18.193405399 + -1 Combine like terms: -18.193405399 + -1 = -19.193405399 n = -19.193405399 Simplifying n = -19.193405399Solution
The solution to the problem is based on the solutions from the subproblems. n = {17.193405399, -19.193405399}
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