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Simplifying 325 = n(120 + -1n) + 50n 325 = (120 * n + -1n * n) + 50n 325 = (120n + -1n2) + 50n Reorder the terms: 325 = 120n + 50n + -1n2 Combine like terms: 120n + 50n = 170n 325 = 170n + -1n2 Solving 325 = 170n + -1n2 Solving for variable 'n'. Reorder the terms: 325 + -170n + n2 = 170n + -170n + -1n2 + n2 Combine like terms: 170n + -170n = 0 325 + -170n + n2 = 0 + -1n2 + n2 325 + -170n + n2 = -1n2 + n2 Combine like terms: -1n2 + n2 = 0 325 + -170n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-325' to each side of the equation. 325 + -170n + -325 + n2 = 0 + -325 Reorder the terms: 325 + -325 + -170n + n2 = 0 + -325 Combine like terms: 325 + -325 = 0 0 + -170n + n2 = 0 + -325 -170n + n2 = 0 + -325 Combine like terms: 0 + -325 = -325 -170n + n2 = -325 The n term is -170n. Take half its coefficient (-85). Square it (7225) and add it to both sides. Add '7225' to each side of the equation. -170n + 7225 + n2 = -325 + 7225 Reorder the terms: 7225 + -170n + n2 = -325 + 7225 Combine like terms: -325 + 7225 = 6900 7225 + -170n + n2 = 6900 Factor a perfect square on the left side: (n + -85)(n + -85) = 6900 Calculate the square root of the right side: 83.066238629 Break this problem into two subproblems by setting (n + -85) equal to 83.066238629 and -83.066238629.Subproblem 1
n + -85 = 83.066238629 Simplifying n + -85 = 83.066238629 Reorder the terms: -85 + n = 83.066238629 Solving -85 + n = 83.066238629 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '85' to each side of the equation. -85 + 85 + n = 83.066238629 + 85 Combine like terms: -85 + 85 = 0 0 + n = 83.066238629 + 85 n = 83.066238629 + 85 Combine like terms: 83.066238629 + 85 = 168.066238629 n = 168.066238629 Simplifying n = 168.066238629Subproblem 2
n + -85 = -83.066238629 Simplifying n + -85 = -83.066238629 Reorder the terms: -85 + n = -83.066238629 Solving -85 + n = -83.066238629 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '85' to each side of the equation. -85 + 85 + n = -83.066238629 + 85 Combine like terms: -85 + 85 = 0 0 + n = -83.066238629 + 85 n = -83.066238629 + 85 Combine like terms: -83.066238629 + 85 = 1.933761371 n = 1.933761371 Simplifying n = 1.933761371Solution
The solution to the problem is based on the solutions from the subproblems. n = {168.066238629, 1.933761371}
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