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Simplifying (n + 2)(n + -5) = 39 Reorder the terms: (2 + n)(n + -5) = 39 Reorder the terms: (2 + n)(-5 + n) = 39 Multiply (2 + n) * (-5 + n) (2(-5 + n) + n(-5 + n)) = 39 ((-5 * 2 + n * 2) + n(-5 + n)) = 39 ((-10 + 2n) + n(-5 + n)) = 39 (-10 + 2n + (-5 * n + n * n)) = 39 (-10 + 2n + (-5n + n2)) = 39 Combine like terms: 2n + -5n = -3n (-10 + -3n + n2) = 39 Solving -10 + -3n + n2 = 39 Solving for variable 'n'. Reorder the terms: -10 + -39 + -3n + n2 = 39 + -39 Combine like terms: -10 + -39 = -49 -49 + -3n + n2 = 39 + -39 Combine like terms: 39 + -39 = 0 -49 + -3n + n2 = 0 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 = 8.658910532 n = 8.658910532 Simplifying n = 8.658910532Subproblem 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 = -5.658910532 n = -5.658910532 Simplifying n = -5.658910532Solution
The solution to the problem is based on the solutions from the subproblems. n = {8.658910532, -5.658910532}
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