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Simplifying n2 + 6n + 27 = 47 Reorder the terms: 27 + 6n + n2 = 47 Solving 27 + 6n + n2 = 47 Solving for variable 'n'. Reorder the terms: 27 + -47 + 6n + n2 = 47 + -47 Combine like terms: 27 + -47 = -20 -20 + 6n + n2 = 47 + -47 Combine like terms: 47 + -47 = 0 -20 + 6n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + 6n + 20 + n2 = 0 + 20 Reorder the terms: -20 + 20 + 6n + n2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 6n + n2 = 0 + 20 6n + n2 = 0 + 20 Combine like terms: 0 + 20 = 20 6n + n2 = 20 The n term is 6n. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6n + 9 + n2 = 20 + 9 Reorder the terms: 9 + 6n + n2 = 20 + 9 Combine like terms: 20 + 9 = 29 9 + 6n + n2 = 29 Factor a perfect square on the left side: (n + 3)(n + 3) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (n + 3) equal to 5.385164807 and -5.385164807.Subproblem 1
n + 3 = 5.385164807 Simplifying n + 3 = 5.385164807 Reorder the terms: 3 + n = 5.385164807 Solving 3 + n = 5.385164807 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + n = 5.385164807 + -3 Combine like terms: 3 + -3 = 0 0 + n = 5.385164807 + -3 n = 5.385164807 + -3 Combine like terms: 5.385164807 + -3 = 2.385164807 n = 2.385164807 Simplifying n = 2.385164807Subproblem 2
n + 3 = -5.385164807 Simplifying n + 3 = -5.385164807 Reorder the terms: 3 + n = -5.385164807 Solving 3 + n = -5.385164807 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + n = -5.385164807 + -3 Combine like terms: 3 + -3 = 0 0 + n = -5.385164807 + -3 n = -5.385164807 + -3 Combine like terms: -5.385164807 + -3 = -8.385164807 n = -8.385164807 Simplifying n = -8.385164807Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.385164807, -8.385164807}
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