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Simplifying n2 + 2n + -108 = 0 Reorder the terms: -108 + 2n + n2 = 0 Solving -108 + 2n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '108' to each side of the equation. -108 + 2n + 108 + n2 = 0 + 108 Reorder the terms: -108 + 108 + 2n + n2 = 0 + 108 Combine like terms: -108 + 108 = 0 0 + 2n + n2 = 0 + 108 2n + n2 = 0 + 108 Combine like terms: 0 + 108 = 108 2n + n2 = 108 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 = 108 + 1 Reorder the terms: 1 + 2n + n2 = 108 + 1 Combine like terms: 108 + 1 = 109 1 + 2n + n2 = 109 Factor a perfect square on the left side: (n + 1)(n + 1) = 109 Calculate the square root of the right side: 10.440306509 Break this problem into two subproblems by setting (n + 1) equal to 10.440306509 and -10.440306509.Subproblem 1
n + 1 = 10.440306509 Simplifying n + 1 = 10.440306509 Reorder the terms: 1 + n = 10.440306509 Solving 1 + n = 10.440306509 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 = 10.440306509 + -1 Combine like terms: 1 + -1 = 0 0 + n = 10.440306509 + -1 n = 10.440306509 + -1 Combine like terms: 10.440306509 + -1 = 9.440306509 n = 9.440306509 Simplifying n = 9.440306509Subproblem 2
n + 1 = -10.440306509 Simplifying n + 1 = -10.440306509 Reorder the terms: 1 + n = -10.440306509 Solving 1 + n = -10.440306509 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 = -10.440306509 + -1 Combine like terms: 1 + -1 = 0 0 + n = -10.440306509 + -1 n = -10.440306509 + -1 Combine like terms: -10.440306509 + -1 = -11.440306509 n = -11.440306509 Simplifying n = -11.440306509Solution
The solution to the problem is based on the solutions from the subproblems. n = {9.440306509, -11.440306509}
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