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Simplifying n2 + -12n + 18 = 0 Reorder the terms: 18 + -12n + n2 = 0 Solving 18 + -12n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + -12n + -18 + n2 = 0 + -18 Reorder the terms: 18 + -18 + -12n + n2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -12n + n2 = 0 + -18 -12n + n2 = 0 + -18 Combine like terms: 0 + -18 = -18 -12n + n2 = -18 The n term is -12n. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12n + 36 + n2 = -18 + 36 Reorder the terms: 36 + -12n + n2 = -18 + 36 Combine like terms: -18 + 36 = 18 36 + -12n + n2 = 18 Factor a perfect square on the left side: (n + -6)(n + -6) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (n + -6) equal to 4.242640687 and -4.242640687.Subproblem 1
n + -6 = 4.242640687 Simplifying n + -6 = 4.242640687 Reorder the terms: -6 + n = 4.242640687 Solving -6 + n = 4.242640687 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + n = 4.242640687 + 6 Combine like terms: -6 + 6 = 0 0 + n = 4.242640687 + 6 n = 4.242640687 + 6 Combine like terms: 4.242640687 + 6 = 10.242640687 n = 10.242640687 Simplifying n = 10.242640687Subproblem 2
n + -6 = -4.242640687 Simplifying n + -6 = -4.242640687 Reorder the terms: -6 + n = -4.242640687 Solving -6 + n = -4.242640687 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + n = -4.242640687 + 6 Combine like terms: -6 + 6 = 0 0 + n = -4.242640687 + 6 n = -4.242640687 + 6 Combine like terms: -4.242640687 + 6 = 1.757359313 n = 1.757359313 Simplifying n = 1.757359313Solution
The solution to the problem is based on the solutions from the subproblems. n = {10.242640687, 1.757359313}
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