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Simplifying n2 + 5n + -30 = 0 Reorder the terms: -30 + 5n + n2 = 0 Solving -30 + 5n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + 5n + 30 + n2 = 0 + 30 Reorder the terms: -30 + 30 + 5n + n2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 5n + n2 = 0 + 30 5n + n2 = 0 + 30 Combine like terms: 0 + 30 = 30 5n + n2 = 30 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 = 30 + 6.25 Reorder the terms: 6.25 + 5n + n2 = 30 + 6.25 Combine like terms: 30 + 6.25 = 36.25 6.25 + 5n + n2 = 36.25 Factor a perfect square on the left side: (n + 2.5)(n + 2.5) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (n + 2.5) equal to 6.020797289 and -6.020797289.Subproblem 1
n + 2.5 = 6.020797289 Simplifying n + 2.5 = 6.020797289 Reorder the terms: 2.5 + n = 6.020797289 Solving 2.5 + n = 6.020797289 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 = 6.020797289 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + n = 6.020797289 + -2.5 n = 6.020797289 + -2.5 Combine like terms: 6.020797289 + -2.5 = 3.520797289 n = 3.520797289 Simplifying n = 3.520797289Subproblem 2
n + 2.5 = -6.020797289 Simplifying n + 2.5 = -6.020797289 Reorder the terms: 2.5 + n = -6.020797289 Solving 2.5 + n = -6.020797289 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 = -6.020797289 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + n = -6.020797289 + -2.5 n = -6.020797289 + -2.5 Combine like terms: -6.020797289 + -2.5 = -8.520797289 n = -8.520797289 Simplifying n = -8.520797289Solution
The solution to the problem is based on the solutions from the subproblems. n = {3.520797289, -8.520797289}
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