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Simplifying n2 + 3n + -49 = 0 Reorder the terms: -49 + 3n + n2 = 0 Solving -49 + 3n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + 3n + 49 + n2 = 0 + 49 Reorder the terms: -49 + 49 + 3n + n2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 3n + n2 = 0 + 49 3n + n2 = 0 + 49 Combine like terms: 0 + 49 = 49 3n + n2 = 49 The n term is 3n. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3n + 2.25 + n2 = 49 + 2.25 Reorder the terms: 2.25 + 3n + n2 = 49 + 2.25 Combine like terms: 49 + 2.25 = 51.25 2.25 + 3n + n2 = 51.25 Factor a perfect square on the left side: (n + 1.5)(n + 1.5) = 51.25 Calculate the square root of the right side: 7.158910532 Break this problem into two subproblems by setting (n + 1.5) equal to 7.158910532 and -7.158910532.Subproblem 1
n + 1.5 = 7.158910532 Simplifying n + 1.5 = 7.158910532 Reorder the terms: 1.5 + n = 7.158910532 Solving 1.5 + n = 7.158910532 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + n = 7.158910532 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + n = 7.158910532 + -1.5 n = 7.158910532 + -1.5 Combine like terms: 7.158910532 + -1.5 = 5.658910532 n = 5.658910532 Simplifying n = 5.658910532Subproblem 2
n + 1.5 = -7.158910532 Simplifying n + 1.5 = -7.158910532 Reorder the terms: 1.5 + n = -7.158910532 Solving 1.5 + n = -7.158910532 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + n = -7.158910532 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + n = -7.158910532 + -1.5 n = -7.158910532 + -1.5 Combine like terms: -7.158910532 + -1.5 = -8.658910532 n = -8.658910532 Simplifying n = -8.658910532Solution
The solution to the problem is based on the solutions from the subproblems. n = {5.658910532, -8.658910532}
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