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Simplifying n2 + -6n + -8 = 0 Reorder the terms: -8 + -6n + n2 = 0 Solving -8 + -6n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -6n + 8 + n2 = 0 + 8 Reorder the terms: -8 + 8 + -6n + n2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -6n + n2 = 0 + 8 -6n + n2 = 0 + 8 Combine like terms: 0 + 8 = 8 -6n + n2 = 8 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 = 8 + 9 Reorder the terms: 9 + -6n + n2 = 8 + 9 Combine like terms: 8 + 9 = 17 9 + -6n + n2 = 17 Factor a perfect square on the left side: (n + -3)(n + -3) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (n + -3) equal to 4.123105626 and -4.123105626.Subproblem 1
n + -3 = 4.123105626 Simplifying n + -3 = 4.123105626 Reorder the terms: -3 + n = 4.123105626 Solving -3 + n = 4.123105626 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 = 4.123105626 + 3 Combine like terms: -3 + 3 = 0 0 + n = 4.123105626 + 3 n = 4.123105626 + 3 Combine like terms: 4.123105626 + 3 = 7.123105626 n = 7.123105626 Simplifying n = 7.123105626Subproblem 2
n + -3 = -4.123105626 Simplifying n + -3 = -4.123105626 Reorder the terms: -3 + n = -4.123105626 Solving -3 + n = -4.123105626 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 = -4.123105626 + 3 Combine like terms: -3 + 3 = 0 0 + n = -4.123105626 + 3 n = -4.123105626 + 3 Combine like terms: -4.123105626 + 3 = -1.123105626 n = -1.123105626 Simplifying n = -1.123105626Solution
The solution to the problem is based on the solutions from the subproblems. n = {7.123105626, -1.123105626}
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