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Simplifying n2 + 2n + -3 = 299 Reorder the terms: -3 + 2n + n2 = 299 Solving -3 + 2n + n2 = 299 Solving for variable 'n'. Reorder the terms: -3 + -299 + 2n + n2 = 299 + -299 Combine like terms: -3 + -299 = -302 -302 + 2n + n2 = 299 + -299 Combine like terms: 299 + -299 = 0 -302 + 2n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '302' to each side of the equation. -302 + 2n + 302 + n2 = 0 + 302 Reorder the terms: -302 + 302 + 2n + n2 = 0 + 302 Combine like terms: -302 + 302 = 0 0 + 2n + n2 = 0 + 302 2n + n2 = 0 + 302 Combine like terms: 0 + 302 = 302 2n + n2 = 302 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 = 302 + 1 Reorder the terms: 1 + 2n + n2 = 302 + 1 Combine like terms: 302 + 1 = 303 1 + 2n + n2 = 303 Factor a perfect square on the left side: (n + 1)(n + 1) = 303 Calculate the square root of the right side: 17.406895186 Break this problem into two subproblems by setting (n + 1) equal to 17.406895186 and -17.406895186.Subproblem 1
n + 1 = 17.406895186 Simplifying n + 1 = 17.406895186 Reorder the terms: 1 + n = 17.406895186 Solving 1 + n = 17.406895186 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 = 17.406895186 + -1 Combine like terms: 1 + -1 = 0 0 + n = 17.406895186 + -1 n = 17.406895186 + -1 Combine like terms: 17.406895186 + -1 = 16.406895186 n = 16.406895186 Simplifying n = 16.406895186Subproblem 2
n + 1 = -17.406895186 Simplifying n + 1 = -17.406895186 Reorder the terms: 1 + n = -17.406895186 Solving 1 + n = -17.406895186 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 = -17.406895186 + -1 Combine like terms: 1 + -1 = 0 0 + n = -17.406895186 + -1 n = -17.406895186 + -1 Combine like terms: -17.406895186 + -1 = -18.406895186 n = -18.406895186 Simplifying n = -18.406895186Solution
The solution to the problem is based on the solutions from the subproblems. n = {16.406895186, -18.406895186}
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