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Simplifying -20n2 + -680n + 48000 = 0 Reorder the terms: 48000 + -680n + -20n2 = 0 Solving 48000 + -680n + -20n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '20'. 20(2400 + -34n + -1n2) = 0 Ignore the factor 20.Subproblem 1
Set the factor '(2400 + -34n + -1n2)' equal to zero and attempt to solve: Simplifying 2400 + -34n + -1n2 = 0 Solving 2400 + -34n + -1n2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2400 + 34n + n2 = 0 Move the constant term to the right: Add '2400' to each side of the equation. -2400 + 34n + 2400 + n2 = 0 + 2400 Reorder the terms: -2400 + 2400 + 34n + n2 = 0 + 2400 Combine like terms: -2400 + 2400 = 0 0 + 34n + n2 = 0 + 2400 34n + n2 = 0 + 2400 Combine like terms: 0 + 2400 = 2400 34n + n2 = 2400 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 = 2400 + 289 Reorder the terms: 289 + 34n + n2 = 2400 + 289 Combine like terms: 2400 + 289 = 2689 289 + 34n + n2 = 2689 Factor a perfect square on the left side: (n + 17)(n + 17) = 2689 Calculate the square root of the right side: 51.85556865 Break this problem into two subproblems by setting (n + 17) equal to 51.85556865 and -51.85556865.Subproblem 1
n + 17 = 51.85556865 Simplifying n + 17 = 51.85556865 Reorder the terms: 17 + n = 51.85556865 Solving 17 + n = 51.85556865 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 = 51.85556865 + -17 Combine like terms: 17 + -17 = 0 0 + n = 51.85556865 + -17 n = 51.85556865 + -17 Combine like terms: 51.85556865 + -17 = 34.85556865 n = 34.85556865 Simplifying n = 34.85556865Subproblem 2
n + 17 = -51.85556865 Simplifying n + 17 = -51.85556865 Reorder the terms: 17 + n = -51.85556865 Solving 17 + n = -51.85556865 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 = -51.85556865 + -17 Combine like terms: 17 + -17 = 0 0 + n = -51.85556865 + -17 n = -51.85556865 + -17 Combine like terms: -51.85556865 + -17 = -68.85556865 n = -68.85556865 Simplifying n = -68.85556865Solution
The solution to the problem is based on the solutions from the subproblems. n = {34.85556865, -68.85556865}Solution
n = {34.85556865, -68.85556865}
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