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Simplifying n2 + 6n = 8 Reorder the terms: 6n + n2 = 8 Solving 6n + n2 = 8 Solving for variable 'n'. Reorder the terms: -8 + 6n + n2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + 6n + n2 = 0 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 = 1.123105626 n = 1.123105626 Simplifying n = 1.123105626Subproblem 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 = -7.123105626 n = -7.123105626 Simplifying n = -7.123105626Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.123105626, -7.123105626}
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