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Simplifying n2 + 5n + -120 = 0 Reorder the terms: -120 + 5n + n2 = 0 Solving -120 + 5n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '120' to each side of the equation. -120 + 5n + 120 + n2 = 0 + 120 Reorder the terms: -120 + 120 + 5n + n2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + 5n + n2 = 0 + 120 5n + n2 = 0 + 120 Combine like terms: 0 + 120 = 120 5n + n2 = 120 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 = 120 + 6.25 Reorder the terms: 6.25 + 5n + n2 = 120 + 6.25 Combine like terms: 120 + 6.25 = 126.25 6.25 + 5n + n2 = 126.25 Factor a perfect square on the left side: (n + 2.5)(n + 2.5) = 126.25 Calculate the square root of the right side: 11.236102527 Break this problem into two subproblems by setting (n + 2.5) equal to 11.236102527 and -11.236102527.Subproblem 1
n + 2.5 = 11.236102527 Simplifying n + 2.5 = 11.236102527 Reorder the terms: 2.5 + n = 11.236102527 Solving 2.5 + n = 11.236102527 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 = 11.236102527 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + n = 11.236102527 + -2.5 n = 11.236102527 + -2.5 Combine like terms: 11.236102527 + -2.5 = 8.736102527 n = 8.736102527 Simplifying n = 8.736102527Subproblem 2
n + 2.5 = -11.236102527 Simplifying n + 2.5 = -11.236102527 Reorder the terms: 2.5 + n = -11.236102527 Solving 2.5 + n = -11.236102527 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 = -11.236102527 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + n = -11.236102527 + -2.5 n = -11.236102527 + -2.5 Combine like terms: -11.236102527 + -2.5 = -13.736102527 n = -13.736102527 Simplifying n = -13.736102527Solution
The solution to the problem is based on the solutions from the subproblems. n = {8.736102527, -13.736102527}
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