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Simplifying n2 + -9n + -40 = -8 + -5 Reorder the terms: -40 + -9n + n2 = -8 + -5 Combine like terms: -8 + -5 = -13 -40 + -9n + n2 = -13 Solving -40 + -9n + n2 = -13 Solving for variable 'n'. Reorder the terms: -40 + 13 + -9n + n2 = -13 + 13 Combine like terms: -40 + 13 = -27 -27 + -9n + n2 = -13 + 13 Combine like terms: -13 + 13 = 0 -27 + -9n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + -9n + 27 + n2 = 0 + 27 Reorder the terms: -27 + 27 + -9n + n2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -9n + n2 = 0 + 27 -9n + n2 = 0 + 27 Combine like terms: 0 + 27 = 27 -9n + n2 = 27 The n term is -9n. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9n + 20.25 + n2 = 27 + 20.25 Reorder the terms: 20.25 + -9n + n2 = 27 + 20.25 Combine like terms: 27 + 20.25 = 47.25 20.25 + -9n + n2 = 47.25 Factor a perfect square on the left side: (n + -4.5)(n + -4.5) = 47.25 Calculate the square root of the right side: 6.873863542 Break this problem into two subproblems by setting (n + -4.5) equal to 6.873863542 and -6.873863542.Subproblem 1
n + -4.5 = 6.873863542 Simplifying n + -4.5 = 6.873863542 Reorder the terms: -4.5 + n = 6.873863542 Solving -4.5 + n = 6.873863542 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + n = 6.873863542 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + n = 6.873863542 + 4.5 n = 6.873863542 + 4.5 Combine like terms: 6.873863542 + 4.5 = 11.373863542 n = 11.373863542 Simplifying n = 11.373863542Subproblem 2
n + -4.5 = -6.873863542 Simplifying n + -4.5 = -6.873863542 Reorder the terms: -4.5 + n = -6.873863542 Solving -4.5 + n = -6.873863542 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + n = -6.873863542 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + n = -6.873863542 + 4.5 n = -6.873863542 + 4.5 Combine like terms: -6.873863542 + 4.5 = -2.373863542 n = -2.373863542 Simplifying n = -2.373863542Solution
The solution to the problem is based on the solutions from the subproblems. n = {11.373863542, -2.373863542}
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