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Simplifying n2 + 5n = 288 Reorder the terms: 5n + n2 = 288 Solving 5n + n2 = 288 Solving for variable 'n'. Reorder the terms: -288 + 5n + n2 = 288 + -288 Combine like terms: 288 + -288 = 0 -288 + 5n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '288' to each side of the equation. -288 + 5n + 288 + n2 = 0 + 288 Reorder the terms: -288 + 288 + 5n + n2 = 0 + 288 Combine like terms: -288 + 288 = 0 0 + 5n + n2 = 0 + 288 5n + n2 = 0 + 288 Combine like terms: 0 + 288 = 288 5n + n2 = 288 The n term is 5n. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5n + 6.25 + n2 = 288 + 6.25 Reorder the terms: 6.25 + 5n + n2 = 288 + 6.25 Combine like terms: 288 + 6.25 = 294.25 6.25 + 5n + n2 = 294.25 Factor a perfect square on the left side: (n + 2.5)(n + 2.5) = 294.25 Calculate the square root of the right side: 17.153716798 Break this problem into two subproblems by setting (n + 2.5) equal to 17.153716798 and -17.153716798.Subproblem 1
n + 2.5 = 17.153716798 Simplifying n + 2.5 = 17.153716798 Reorder the terms: 2.5 + n = 17.153716798 Solving 2.5 + n = 17.153716798 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + n = 17.153716798 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + n = 17.153716798 + -2.5 n = 17.153716798 + -2.5 Combine like terms: 17.153716798 + -2.5 = 14.653716798 n = 14.653716798 Simplifying n = 14.653716798Subproblem 2
n + 2.5 = -17.153716798 Simplifying n + 2.5 = -17.153716798 Reorder the terms: 2.5 + n = -17.153716798 Solving 2.5 + n = -17.153716798 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + n = -17.153716798 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + n = -17.153716798 + -2.5 n = -17.153716798 + -2.5 Combine like terms: -17.153716798 + -2.5 = -19.653716798 n = -19.653716798 Simplifying n = -19.653716798Solution
The solution to the problem is based on the solutions from the subproblems. n = {14.653716798, -19.653716798}
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