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Simplifying n2 + 50n + 25 = 0 Reorder the terms: 25 + 50n + n2 = 0 Solving 25 + 50n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + 50n + -25 + n2 = 0 + -25 Reorder the terms: 25 + -25 + 50n + n2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 50n + n2 = 0 + -25 50n + n2 = 0 + -25 Combine like terms: 0 + -25 = -25 50n + n2 = -25 The n term is 50n. Take half its coefficient (25). Square it (625) and add it to both sides. Add '625' to each side of the equation. 50n + 625 + n2 = -25 + 625 Reorder the terms: 625 + 50n + n2 = -25 + 625 Combine like terms: -25 + 625 = 600 625 + 50n + n2 = 600 Factor a perfect square on the left side: (n + 25)(n + 25) = 600 Calculate the square root of the right side: 24.494897428 Break this problem into two subproblems by setting (n + 25) equal to 24.494897428 and -24.494897428.Subproblem 1
n + 25 = 24.494897428 Simplifying n + 25 = 24.494897428 Reorder the terms: 25 + n = 24.494897428 Solving 25 + n = 24.494897428 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + n = 24.494897428 + -25 Combine like terms: 25 + -25 = 0 0 + n = 24.494897428 + -25 n = 24.494897428 + -25 Combine like terms: 24.494897428 + -25 = -0.505102572 n = -0.505102572 Simplifying n = -0.505102572Subproblem 2
n + 25 = -24.494897428 Simplifying n + 25 = -24.494897428 Reorder the terms: 25 + n = -24.494897428 Solving 25 + n = -24.494897428 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + n = -24.494897428 + -25 Combine like terms: 25 + -25 = 0 0 + n = -24.494897428 + -25 n = -24.494897428 + -25 Combine like terms: -24.494897428 + -25 = -49.494897428 n = -49.494897428 Simplifying n = -49.494897428Solution
The solution to the problem is based on the solutions from the subproblems. n = {-0.505102572, -49.494897428}
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