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Simplifying 2n3 + -2880n2 + -24482n = 0 Reorder the terms: -24482n + -2880n2 + 2n3 = 0 Solving -24482n + -2880n2 + 2n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2n'. 2n(-12241 + -1440n + n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n = 0Subproblem 2
Set the factor '(-12241 + -1440n + n2)' equal to zero and attempt to solve: Simplifying -12241 + -1440n + n2 = 0 Solving -12241 + -1440n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '12241' to each side of the equation. -12241 + -1440n + 12241 + n2 = 0 + 12241 Reorder the terms: -12241 + 12241 + -1440n + n2 = 0 + 12241 Combine like terms: -12241 + 12241 = 0 0 + -1440n + n2 = 0 + 12241 -1440n + n2 = 0 + 12241 Combine like terms: 0 + 12241 = 12241 -1440n + n2 = 12241 The n term is -1440n. Take half its coefficient (-720). Square it (518400) and add it to both sides. Add '518400' to each side of the equation. -1440n + 518400 + n2 = 12241 + 518400 Reorder the terms: 518400 + -1440n + n2 = 12241 + 518400 Combine like terms: 12241 + 518400 = 530641 518400 + -1440n + n2 = 530641 Factor a perfect square on the left side: (n + -720)(n + -720) = 530641 Calculate the square root of the right side: 728.451096505 Break this problem into two subproblems by setting (n + -720) equal to 728.451096505 and -728.451096505.Subproblem 1
n + -720 = 728.451096505 Simplifying n + -720 = 728.451096505 Reorder the terms: -720 + n = 728.451096505 Solving -720 + n = 728.451096505 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '720' to each side of the equation. -720 + 720 + n = 728.451096505 + 720 Combine like terms: -720 + 720 = 0 0 + n = 728.451096505 + 720 n = 728.451096505 + 720 Combine like terms: 728.451096505 + 720 = 1448.451096505 n = 1448.451096505 Simplifying n = 1448.451096505Subproblem 2
n + -720 = -728.451096505 Simplifying n + -720 = -728.451096505 Reorder the terms: -720 + n = -728.451096505 Solving -720 + n = -728.451096505 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '720' to each side of the equation. -720 + 720 + n = -728.451096505 + 720 Combine like terms: -720 + 720 = 0 0 + n = -728.451096505 + 720 n = -728.451096505 + 720 Combine like terms: -728.451096505 + 720 = -8.451096505 n = -8.451096505 Simplifying n = -8.451096505Solution
The solution to the problem is based on the solutions from the subproblems. n = {1448.451096505, -8.451096505}Solution
n = {0, 1448.451096505, -8.451096505}
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