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Simplifying n2 + 3n = 60 Reorder the terms: 3n + n2 = 60 Solving 3n + n2 = 60 Solving for variable 'n'. Reorder the terms: -60 + 3n + n2 = 60 + -60 Combine like terms: 60 + -60 = 0 -60 + 3n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + 3n + 60 + n2 = 0 + 60 Reorder the terms: -60 + 60 + 3n + n2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 3n + n2 = 0 + 60 3n + n2 = 0 + 60 Combine like terms: 0 + 60 = 60 3n + n2 = 60 The n term is 3n. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3n + 2.25 + n2 = 60 + 2.25 Reorder the terms: 2.25 + 3n + n2 = 60 + 2.25 Combine like terms: 60 + 2.25 = 62.25 2.25 + 3n + n2 = 62.25 Factor a perfect square on the left side: (n + 1.5)(n + 1.5) = 62.25 Calculate the square root of the right side: 7.889866919 Break this problem into two subproblems by setting (n + 1.5) equal to 7.889866919 and -7.889866919.Subproblem 1
n + 1.5 = 7.889866919 Simplifying n + 1.5 = 7.889866919 Reorder the terms: 1.5 + n = 7.889866919 Solving 1.5 + n = 7.889866919 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + n = 7.889866919 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + n = 7.889866919 + -1.5 n = 7.889866919 + -1.5 Combine like terms: 7.889866919 + -1.5 = 6.389866919 n = 6.389866919 Simplifying n = 6.389866919Subproblem 2
n + 1.5 = -7.889866919 Simplifying n + 1.5 = -7.889866919 Reorder the terms: 1.5 + n = -7.889866919 Solving 1.5 + n = -7.889866919 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + n = -7.889866919 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + n = -7.889866919 + -1.5 n = -7.889866919 + -1.5 Combine like terms: -7.889866919 + -1.5 = -9.389866919 n = -9.389866919 Simplifying n = -9.389866919Solution
The solution to the problem is based on the solutions from the subproblems. n = {6.389866919, -9.389866919}
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