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Simplifying n2 + -50n + 3 = 0 Reorder the terms: 3 + -50n + n2 = 0 Solving 3 + -50n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -50n + -3 + n2 = 0 + -3 Reorder the terms: 3 + -3 + -50n + n2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -50n + n2 = 0 + -3 -50n + n2 = 0 + -3 Combine like terms: 0 + -3 = -3 -50n + n2 = -3 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 = -3 + 625 Reorder the terms: 625 + -50n + n2 = -3 + 625 Combine like terms: -3 + 625 = 622 625 + -50n + n2 = 622 Factor a perfect square on the left side: (n + -25)(n + -25) = 622 Calculate the square root of the right side: 24.939927827 Break this problem into two subproblems by setting (n + -25) equal to 24.939927827 and -24.939927827.Subproblem 1
n + -25 = 24.939927827 Simplifying n + -25 = 24.939927827 Reorder the terms: -25 + n = 24.939927827 Solving -25 + n = 24.939927827 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 = 24.939927827 + 25 Combine like terms: -25 + 25 = 0 0 + n = 24.939927827 + 25 n = 24.939927827 + 25 Combine like terms: 24.939927827 + 25 = 49.939927827 n = 49.939927827 Simplifying n = 49.939927827Subproblem 2
n + -25 = -24.939927827 Simplifying n + -25 = -24.939927827 Reorder the terms: -25 + n = -24.939927827 Solving -25 + n = -24.939927827 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 = -24.939927827 + 25 Combine like terms: -25 + 25 = 0 0 + n = -24.939927827 + 25 n = -24.939927827 + 25 Combine like terms: -24.939927827 + 25 = 0.060072173 n = 0.060072173 Simplifying n = 0.060072173Solution
The solution to the problem is based on the solutions from the subproblems. n = {49.939927827, 0.060072173}
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