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Simplifying n2 + 6n + -18 = 5 Reorder the terms: -18 + 6n + n2 = 5 Solving -18 + 6n + n2 = 5 Solving for variable 'n'. Reorder the terms: -18 + -5 + 6n + n2 = 5 + -5 Combine like terms: -18 + -5 = -23 -23 + 6n + n2 = 5 + -5 Combine like terms: 5 + -5 = 0 -23 + 6n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + 6n + 23 + n2 = 0 + 23 Reorder the terms: -23 + 23 + 6n + n2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + 6n + n2 = 0 + 23 6n + n2 = 0 + 23 Combine like terms: 0 + 23 = 23 6n + n2 = 23 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 = 23 + 9 Reorder the terms: 9 + 6n + n2 = 23 + 9 Combine like terms: 23 + 9 = 32 9 + 6n + n2 = 32 Factor a perfect square on the left side: (n + 3)(n + 3) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (n + 3) equal to 5.656854249 and -5.656854249.Subproblem 1
n + 3 = 5.656854249 Simplifying n + 3 = 5.656854249 Reorder the terms: 3 + n = 5.656854249 Solving 3 + n = 5.656854249 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 = 5.656854249 + -3 Combine like terms: 3 + -3 = 0 0 + n = 5.656854249 + -3 n = 5.656854249 + -3 Combine like terms: 5.656854249 + -3 = 2.656854249 n = 2.656854249 Simplifying n = 2.656854249Subproblem 2
n + 3 = -5.656854249 Simplifying n + 3 = -5.656854249 Reorder the terms: 3 + n = -5.656854249 Solving 3 + n = -5.656854249 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 = -5.656854249 + -3 Combine like terms: 3 + -3 = 0 0 + n = -5.656854249 + -3 n = -5.656854249 + -3 Combine like terms: -5.656854249 + -3 = -8.656854249 n = -8.656854249 Simplifying n = -8.656854249Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.656854249, -8.656854249}
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