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Simplifying n2 + 30n + 120 = 0 Reorder the terms: 120 + 30n + n2 = 0 Solving 120 + 30n + 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 + 30n + -120 + n2 = 0 + -120 Reorder the terms: 120 + -120 + 30n + n2 = 0 + -120 Combine like terms: 120 + -120 = 0 0 + 30n + n2 = 0 + -120 30n + n2 = 0 + -120 Combine like terms: 0 + -120 = -120 30n + n2 = -120 The n term is 30n. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30n + 225 + n2 = -120 + 225 Reorder the terms: 225 + 30n + n2 = -120 + 225 Combine like terms: -120 + 225 = 105 225 + 30n + n2 = 105 Factor a perfect square on the left side: (n + 15)(n + 15) = 105 Calculate the square root of the right side: 10.246950766 Break this problem into two subproblems by setting (n + 15) equal to 10.246950766 and -10.246950766.Subproblem 1
n + 15 = 10.246950766 Simplifying n + 15 = 10.246950766 Reorder the terms: 15 + n = 10.246950766 Solving 15 + n = 10.246950766 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + n = 10.246950766 + -15 Combine like terms: 15 + -15 = 0 0 + n = 10.246950766 + -15 n = 10.246950766 + -15 Combine like terms: 10.246950766 + -15 = -4.753049234 n = -4.753049234 Simplifying n = -4.753049234Subproblem 2
n + 15 = -10.246950766 Simplifying n + 15 = -10.246950766 Reorder the terms: 15 + n = -10.246950766 Solving 15 + n = -10.246950766 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + n = -10.246950766 + -15 Combine like terms: 15 + -15 = 0 0 + n = -10.246950766 + -15 n = -10.246950766 + -15 Combine like terms: -10.246950766 + -15 = -25.246950766 n = -25.246950766 Simplifying n = -25.246950766Solution
The solution to the problem is based on the solutions from the subproblems. n = {-4.753049234, -25.246950766}
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