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Simplifying n2 + 60n + -336 = 0 Reorder the terms: -336 + 60n + n2 = 0 Solving -336 + 60n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '336' to each side of the equation. -336 + 60n + 336 + n2 = 0 + 336 Reorder the terms: -336 + 336 + 60n + n2 = 0 + 336 Combine like terms: -336 + 336 = 0 0 + 60n + n2 = 0 + 336 60n + n2 = 0 + 336 Combine like terms: 0 + 336 = 336 60n + n2 = 336 The n term is 60n. Take half its coefficient (30). Square it (900) and add it to both sides. Add '900' to each side of the equation. 60n + 900 + n2 = 336 + 900 Reorder the terms: 900 + 60n + n2 = 336 + 900 Combine like terms: 336 + 900 = 1236 900 + 60n + n2 = 1236 Factor a perfect square on the left side: (n + 30)(n + 30) = 1236 Calculate the square root of the right side: 35.156791662 Break this problem into two subproblems by setting (n + 30) equal to 35.156791662 and -35.156791662.Subproblem 1
n + 30 = 35.156791662 Simplifying n + 30 = 35.156791662 Reorder the terms: 30 + n = 35.156791662 Solving 30 + n = 35.156791662 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + n = 35.156791662 + -30 Combine like terms: 30 + -30 = 0 0 + n = 35.156791662 + -30 n = 35.156791662 + -30 Combine like terms: 35.156791662 + -30 = 5.156791662 n = 5.156791662 Simplifying n = 5.156791662Subproblem 2
n + 30 = -35.156791662 Simplifying n + 30 = -35.156791662 Reorder the terms: 30 + n = -35.156791662 Solving 30 + n = -35.156791662 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + n = -35.156791662 + -30 Combine like terms: 30 + -30 = 0 0 + n = -35.156791662 + -30 n = -35.156791662 + -30 Combine like terms: -35.156791662 + -30 = -65.156791662 n = -65.156791662 Simplifying n = -65.156791662Solution
The solution to the problem is based on the solutions from the subproblems. n = {5.156791662, -65.156791662}
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