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Simplifying n2 + 19n + -40 = 0 Reorder the terms: -40 + 19n + n2 = 0 Solving -40 + 19n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + 19n + 40 + n2 = 0 + 40 Reorder the terms: -40 + 40 + 19n + n2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 19n + n2 = 0 + 40 19n + n2 = 0 + 40 Combine like terms: 0 + 40 = 40 19n + n2 = 40 The n term is 19n. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19n + 90.25 + n2 = 40 + 90.25 Reorder the terms: 90.25 + 19n + n2 = 40 + 90.25 Combine like terms: 40 + 90.25 = 130.25 90.25 + 19n + n2 = 130.25 Factor a perfect square on the left side: (n + 9.5)(n + 9.5) = 130.25 Calculate the square root of the right side: 11.412712211 Break this problem into two subproblems by setting (n + 9.5) equal to 11.412712211 and -11.412712211.Subproblem 1
n + 9.5 = 11.412712211 Simplifying n + 9.5 = 11.412712211 Reorder the terms: 9.5 + n = 11.412712211 Solving 9.5 + n = 11.412712211 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + n = 11.412712211 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + n = 11.412712211 + -9.5 n = 11.412712211 + -9.5 Combine like terms: 11.412712211 + -9.5 = 1.912712211 n = 1.912712211 Simplifying n = 1.912712211Subproblem 2
n + 9.5 = -11.412712211 Simplifying n + 9.5 = -11.412712211 Reorder the terms: 9.5 + n = -11.412712211 Solving 9.5 + n = -11.412712211 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + n = -11.412712211 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + n = -11.412712211 + -9.5 n = -11.412712211 + -9.5 Combine like terms: -11.412712211 + -9.5 = -20.912712211 n = -20.912712211 Simplifying n = -20.912712211Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.912712211, -20.912712211}
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