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Simplifying n2 + 8n + -400 = 0 Reorder the terms: -400 + 8n + n2 = 0 Solving -400 + 8n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '400' to each side of the equation. -400 + 8n + 400 + n2 = 0 + 400 Reorder the terms: -400 + 400 + 8n + n2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + 8n + n2 = 0 + 400 8n + n2 = 0 + 400 Combine like terms: 0 + 400 = 400 8n + n2 = 400 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 = 400 + 16 Reorder the terms: 16 + 8n + n2 = 400 + 16 Combine like terms: 400 + 16 = 416 16 + 8n + n2 = 416 Factor a perfect square on the left side: (n + 4)(n + 4) = 416 Calculate the square root of the right side: 20.396078054 Break this problem into two subproblems by setting (n + 4) equal to 20.396078054 and -20.396078054.Subproblem 1
n + 4 = 20.396078054 Simplifying n + 4 = 20.396078054 Reorder the terms: 4 + n = 20.396078054 Solving 4 + n = 20.396078054 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 = 20.396078054 + -4 Combine like terms: 4 + -4 = 0 0 + n = 20.396078054 + -4 n = 20.396078054 + -4 Combine like terms: 20.396078054 + -4 = 16.396078054 n = 16.396078054 Simplifying n = 16.396078054Subproblem 2
n + 4 = -20.396078054 Simplifying n + 4 = -20.396078054 Reorder the terms: 4 + n = -20.396078054 Solving 4 + n = -20.396078054 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 = -20.396078054 + -4 Combine like terms: 4 + -4 = 0 0 + n = -20.396078054 + -4 n = -20.396078054 + -4 Combine like terms: -20.396078054 + -4 = -24.396078054 n = -24.396078054 Simplifying n = -24.396078054Solution
The solution to the problem is based on the solutions from the subproblems. n = {16.396078054, -24.396078054}
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