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Simplifying n2 + -2n + -18 = 8 Reorder the terms: -18 + -2n + n2 = 8 Solving -18 + -2n + n2 = 8 Solving for variable 'n'. Reorder the terms: -18 + -8 + -2n + n2 = 8 + -8 Combine like terms: -18 + -8 = -26 -26 + -2n + n2 = 8 + -8 Combine like terms: 8 + -8 = 0 -26 + -2n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '26' to each side of the equation. -26 + -2n + 26 + n2 = 0 + 26 Reorder the terms: -26 + 26 + -2n + n2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + -2n + n2 = 0 + 26 -2n + n2 = 0 + 26 Combine like terms: 0 + 26 = 26 -2n + n2 = 26 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 = 26 + 1 Reorder the terms: 1 + -2n + n2 = 26 + 1 Combine like terms: 26 + 1 = 27 1 + -2n + n2 = 27 Factor a perfect square on the left side: (n + -1)(n + -1) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (n + -1) equal to 5.196152423 and -5.196152423.Subproblem 1
n + -1 = 5.196152423 Simplifying n + -1 = 5.196152423 Reorder the terms: -1 + n = 5.196152423 Solving -1 + n = 5.196152423 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 = 5.196152423 + 1 Combine like terms: -1 + 1 = 0 0 + n = 5.196152423 + 1 n = 5.196152423 + 1 Combine like terms: 5.196152423 + 1 = 6.196152423 n = 6.196152423 Simplifying n = 6.196152423Subproblem 2
n + -1 = -5.196152423 Simplifying n + -1 = -5.196152423 Reorder the terms: -1 + n = -5.196152423 Solving -1 + n = -5.196152423 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 = -5.196152423 + 1 Combine like terms: -1 + 1 = 0 0 + n = -5.196152423 + 1 n = -5.196152423 + 1 Combine like terms: -5.196152423 + 1 = -4.196152423 n = -4.196152423 Simplifying n = -4.196152423Solution
The solution to the problem is based on the solutions from the subproblems. n = {6.196152423, -4.196152423}
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