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Simplifying n2 + -25n + 2 = 0 Reorder the terms: 2 + -25n + n2 = 0 Solving 2 + -25n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -25n + -2 + n2 = 0 + -2 Reorder the terms: 2 + -2 + -25n + n2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -25n + n2 = 0 + -2 -25n + n2 = 0 + -2 Combine like terms: 0 + -2 = -2 -25n + n2 = -2 The n term is -25n. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25n + 156.25 + n2 = -2 + 156.25 Reorder the terms: 156.25 + -25n + n2 = -2 + 156.25 Combine like terms: -2 + 156.25 = 154.25 156.25 + -25n + n2 = 154.25 Factor a perfect square on the left side: (n + -12.5)(n + -12.5) = 154.25 Calculate the square root of the right side: 12.419742348 Break this problem into two subproblems by setting (n + -12.5) equal to 12.419742348 and -12.419742348.Subproblem 1
n + -12.5 = 12.419742348 Simplifying n + -12.5 = 12.419742348 Reorder the terms: -12.5 + n = 12.419742348 Solving -12.5 + n = 12.419742348 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + n = 12.419742348 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + n = 12.419742348 + 12.5 n = 12.419742348 + 12.5 Combine like terms: 12.419742348 + 12.5 = 24.919742348 n = 24.919742348 Simplifying n = 24.919742348Subproblem 2
n + -12.5 = -12.419742348 Simplifying n + -12.5 = -12.419742348 Reorder the terms: -12.5 + n = -12.419742348 Solving -12.5 + n = -12.419742348 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + n = -12.419742348 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + n = -12.419742348 + 12.5 n = -12.419742348 + 12.5 Combine like terms: -12.419742348 + 12.5 = 0.080257652 n = 0.080257652 Simplifying n = 0.080257652Solution
The solution to the problem is based on the solutions from the subproblems. n = {24.919742348, 0.080257652}
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