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Simplifying n2 + 2n + -19 = 0 Reorder the terms: -19 + 2n + n2 = 0 Solving -19 + 2n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + 2n + 19 + n2 = 0 + 19 Reorder the terms: -19 + 19 + 2n + n2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 2n + n2 = 0 + 19 2n + n2 = 0 + 19 Combine like terms: 0 + 19 = 19 2n + n2 = 19 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 = 19 + 1 Reorder the terms: 1 + 2n + n2 = 19 + 1 Combine like terms: 19 + 1 = 20 1 + 2n + n2 = 20 Factor a perfect square on the left side: (n + 1)(n + 1) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (n + 1) equal to 4.472135955 and -4.472135955.Subproblem 1
n + 1 = 4.472135955 Simplifying n + 1 = 4.472135955 Reorder the terms: 1 + n = 4.472135955 Solving 1 + n = 4.472135955 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 = 4.472135955 + -1 Combine like terms: 1 + -1 = 0 0 + n = 4.472135955 + -1 n = 4.472135955 + -1 Combine like terms: 4.472135955 + -1 = 3.472135955 n = 3.472135955 Simplifying n = 3.472135955Subproblem 2
n + 1 = -4.472135955 Simplifying n + 1 = -4.472135955 Reorder the terms: 1 + n = -4.472135955 Solving 1 + n = -4.472135955 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 = -4.472135955 + -1 Combine like terms: 1 + -1 = 0 0 + n = -4.472135955 + -1 n = -4.472135955 + -1 Combine like terms: -4.472135955 + -1 = -5.472135955 n = -5.472135955 Simplifying n = -5.472135955Solution
The solution to the problem is based on the solutions from the subproblems. n = {3.472135955, -5.472135955}
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