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Simplifying (18 + 1n)(800 + 50n) = 12650 Multiply (18 + 1n) * (800 + 50n) (18(800 + 50n) + 1n * (800 + 50n)) = 12650 ((800 * 18 + 50n * 18) + 1n * (800 + 50n)) = 12650 ((14400 + 900n) + 1n * (800 + 50n)) = 12650 (14400 + 900n + (800 * 1n + 50n * 1n)) = 12650 (14400 + 900n + (800n + 50n2)) = 12650 Combine like terms: 900n + 800n = 1700n (14400 + 1700n + 50n2) = 12650 Solving 14400 + 1700n + 50n2 = 12650 Solving for variable 'n'. Reorder the terms: 14400 + -12650 + 1700n + 50n2 = 12650 + -12650 Combine like terms: 14400 + -12650 = 1750 1750 + 1700n + 50n2 = 12650 + -12650 Combine like terms: 12650 + -12650 = 0 1750 + 1700n + 50n2 = 0 Factor out the Greatest Common Factor (GCF), '50'. 50(35 + 34n + n2) = 0 Ignore the factor 50.Subproblem 1
Set the factor '(35 + 34n + n2)' equal to zero and attempt to solve: Simplifying 35 + 34n + n2 = 0 Solving 35 + 34n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-35' to each side of the equation. 35 + 34n + -35 + n2 = 0 + -35 Reorder the terms: 35 + -35 + 34n + n2 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + 34n + n2 = 0 + -35 34n + n2 = 0 + -35 Combine like terms: 0 + -35 = -35 34n + n2 = -35 The n term is 34n. Take half its coefficient (17). Square it (289) and add it to both sides. Add '289' to each side of the equation. 34n + 289 + n2 = -35 + 289 Reorder the terms: 289 + 34n + n2 = -35 + 289 Combine like terms: -35 + 289 = 254 289 + 34n + n2 = 254 Factor a perfect square on the left side: (n + 17)(n + 17) = 254 Calculate the square root of the right side: 15.937377451 Break this problem into two subproblems by setting (n + 17) equal to 15.937377451 and -15.937377451.Subproblem 1
n + 17 = 15.937377451 Simplifying n + 17 = 15.937377451 Reorder the terms: 17 + n = 15.937377451 Solving 17 + n = 15.937377451 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + n = 15.937377451 + -17 Combine like terms: 17 + -17 = 0 0 + n = 15.937377451 + -17 n = 15.937377451 + -17 Combine like terms: 15.937377451 + -17 = -1.062622549 n = -1.062622549 Simplifying n = -1.062622549Subproblem 2
n + 17 = -15.937377451 Simplifying n + 17 = -15.937377451 Reorder the terms: 17 + n = -15.937377451 Solving 17 + n = -15.937377451 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + n = -15.937377451 + -17 Combine like terms: 17 + -17 = 0 0 + n = -15.937377451 + -17 n = -15.937377451 + -17 Combine like terms: -15.937377451 + -17 = -32.937377451 n = -32.937377451 Simplifying n = -32.937377451Solution
The solution to the problem is based on the solutions from the subproblems. n = {-1.062622549, -32.937377451}Solution
n = {-1.062622549, -32.937377451}
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