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Simplifying n2 + n = 40 Reorder the terms: n + n2 = 40 Solving n + n2 = 40 Solving for variable 'n'. Reorder the terms: -40 + n + n2 = 40 + -40 Combine like terms: 40 + -40 = 0 -40 + n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + n + 40 + n2 = 0 + 40 Reorder the terms: -40 + 40 + n + n2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + n + n2 = 0 + 40 n + n2 = 0 + 40 Combine like terms: 0 + 40 = 40 n + n2 = 40 The n term is n. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. n + 0.25 + n2 = 40 + 0.25 Reorder the terms: 0.25 + n + n2 = 40 + 0.25 Combine like terms: 40 + 0.25 = 40.25 0.25 + n + n2 = 40.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (n + 0.5) equal to 6.34428877 and -6.34428877.Subproblem 1
n + 0.5 = 6.34428877 Simplifying n + 0.5 = 6.34428877 Reorder the terms: 0.5 + n = 6.34428877 Solving 0.5 + n = 6.34428877 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = 6.34428877 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 6.34428877 + -0.5 n = 6.34428877 + -0.5 Combine like terms: 6.34428877 + -0.5 = 5.84428877 n = 5.84428877 Simplifying n = 5.84428877Subproblem 2
n + 0.5 = -6.34428877 Simplifying n + 0.5 = -6.34428877 Reorder the terms: 0.5 + n = -6.34428877 Solving 0.5 + n = -6.34428877 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = -6.34428877 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -6.34428877 + -0.5 n = -6.34428877 + -0.5 Combine like terms: -6.34428877 + -0.5 = -6.84428877 n = -6.84428877 Simplifying n = -6.84428877Solution
The solution to the problem is based on the solutions from the subproblems. n = {5.84428877, -6.84428877}
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