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Simplifying n2 + 3n + -2352 = 0 Reorder the terms: -2352 + 3n + n2 = 0 Solving -2352 + 3n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '2352' to each side of the equation. -2352 + 3n + 2352 + n2 = 0 + 2352 Reorder the terms: -2352 + 2352 + 3n + n2 = 0 + 2352 Combine like terms: -2352 + 2352 = 0 0 + 3n + n2 = 0 + 2352 3n + n2 = 0 + 2352 Combine like terms: 0 + 2352 = 2352 3n + n2 = 2352 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 = 2352 + 2.25 Reorder the terms: 2.25 + 3n + n2 = 2352 + 2.25 Combine like terms: 2352 + 2.25 = 2354.25 2.25 + 3n + n2 = 2354.25 Factor a perfect square on the left side: (n + 1.5)(n + 1.5) = 2354.25 Calculate the square root of the right side: 48.520614176 Break this problem into two subproblems by setting (n + 1.5) equal to 48.520614176 and -48.520614176.Subproblem 1
n + 1.5 = 48.520614176 Simplifying n + 1.5 = 48.520614176 Reorder the terms: 1.5 + n = 48.520614176 Solving 1.5 + n = 48.520614176 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 = 48.520614176 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + n = 48.520614176 + -1.5 n = 48.520614176 + -1.5 Combine like terms: 48.520614176 + -1.5 = 47.020614176 n = 47.020614176 Simplifying n = 47.020614176Subproblem 2
n + 1.5 = -48.520614176 Simplifying n + 1.5 = -48.520614176 Reorder the terms: 1.5 + n = -48.520614176 Solving 1.5 + n = -48.520614176 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 = -48.520614176 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + n = -48.520614176 + -1.5 n = -48.520614176 + -1.5 Combine like terms: -48.520614176 + -1.5 = -50.020614176 n = -50.020614176 Simplifying n = -50.020614176Solution
The solution to the problem is based on the solutions from the subproblems. n = {47.020614176, -50.020614176}
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