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Simplifying n2 + 2n = 28 Reorder the terms: 2n + n2 = 28 Solving 2n + n2 = 28 Solving for variable 'n'. Reorder the terms: -28 + 2n + n2 = 28 + -28 Combine like terms: 28 + -28 = 0 -28 + 2n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + 2n + 28 + n2 = 0 + 28 Reorder the terms: -28 + 28 + 2n + n2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 2n + n2 = 0 + 28 2n + n2 = 0 + 28 Combine like terms: 0 + 28 = 28 2n + n2 = 28 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 = 28 + 1 Reorder the terms: 1 + 2n + n2 = 28 + 1 Combine like terms: 28 + 1 = 29 1 + 2n + n2 = 29 Factor a perfect square on the left side: (n + 1)(n + 1) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (n + 1) equal to 5.385164807 and -5.385164807.Subproblem 1
n + 1 = 5.385164807 Simplifying n + 1 = 5.385164807 Reorder the terms: 1 + n = 5.385164807 Solving 1 + n = 5.385164807 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 = 5.385164807 + -1 Combine like terms: 1 + -1 = 0 0 + n = 5.385164807 + -1 n = 5.385164807 + -1 Combine like terms: 5.385164807 + -1 = 4.385164807 n = 4.385164807 Simplifying n = 4.385164807Subproblem 2
n + 1 = -5.385164807 Simplifying n + 1 = -5.385164807 Reorder the terms: 1 + n = -5.385164807 Solving 1 + n = -5.385164807 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 = -5.385164807 + -1 Combine like terms: 1 + -1 = 0 0 + n = -5.385164807 + -1 n = -5.385164807 + -1 Combine like terms: -5.385164807 + -1 = -6.385164807 n = -6.385164807 Simplifying n = -6.385164807Solution
The solution to the problem is based on the solutions from the subproblems. n = {4.385164807, -6.385164807}
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