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Simplifying (N + 4)(N + 4) = 104.04 Reorder the terms: (4 + N)(N + 4) = 104.04 Reorder the terms: (4 + N)(4 + N) = 104.04 Multiply (4 + N) * (4 + N) (4(4 + N) + N(4 + N)) = 104.04 ((4 * 4 + N * 4) + N(4 + N)) = 104.04 ((16 + 4N) + N(4 + N)) = 104.04 (16 + 4N + (4 * N + N * N)) = 104.04 (16 + 4N + (4N + N2)) = 104.04 Combine like terms: 4N + 4N = 8N (16 + 8N + N2) = 104.04 Solving 16 + 8N + N2 = 104.04 Solving for variable 'N'. Reorder the terms: 16 + -104.04 + 8N + N2 = 104.04 + -104.04 Combine like terms: 16 + -104.04 = -88.04 -88.04 + 8N + N2 = 104.04 + -104.04 Combine like terms: 104.04 + -104.04 = 0.00 -88.04 + 8N + N2 = 0.00 Begin completing the square. Move the constant term to the right: Add '88.04' to each side of the equation. -88.04 + 8N + 88.04 + N2 = 0.00 + 88.04 Reorder the terms: -88.04 + 88.04 + 8N + N2 = 0.00 + 88.04 Combine like terms: -88.04 + 88.04 = 0.00 0.00 + 8N + N2 = 0.00 + 88.04 8N + N2 = 0.00 + 88.04 Combine like terms: 0.00 + 88.04 = 88.04 8N + N2 = 88.04 The N term is 8N. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8N + 16 + N2 = 88.04 + 16 Reorder the terms: 16 + 8N + N2 = 88.04 + 16 Combine like terms: 88.04 + 16 = 104.04 16 + 8N + N2 = 104.04 Factor a perfect square on the left side: (N + 4)(N + 4) = 104.04 Calculate the square root of the right side: 10.2 Break this problem into two subproblems by setting (N + 4) equal to 10.2 and -10.2.Subproblem 1
N + 4 = 10.2 Simplifying N + 4 = 10.2 Reorder the terms: 4 + N = 10.2 Solving 4 + N = 10.2 Solving for variable 'N'. Move all terms containing N to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + N = 10.2 + -4 Combine like terms: 4 + -4 = 0 0 + N = 10.2 + -4 N = 10.2 + -4 Combine like terms: 10.2 + -4 = 6.2 N = 6.2 Simplifying N = 6.2Subproblem 2
N + 4 = -10.2 Simplifying N + 4 = -10.2 Reorder the terms: 4 + N = -10.2 Solving 4 + N = -10.2 Solving for variable 'N'. Move all terms containing N to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + N = -10.2 + -4 Combine like terms: 4 + -4 = 0 0 + N = -10.2 + -4 N = -10.2 + -4 Combine like terms: -10.2 + -4 = -14.2 N = -14.2 Simplifying N = -14.2Solution
The solution to the problem is based on the solutions from the subproblems. N = {6.2, -14.2}
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