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Simplifying 14n5 + -42n4 + -70n3 = 0 Reorder the terms: -70n3 + -42n4 + 14n5 = 0 Solving -70n3 + -42n4 + 14n5 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '14n3'. 14n3(-5 + -3n + n2) = 0 Ignore the factor 14.Subproblem 1
Set the factor 'n3' equal to zero and attempt to solve: Simplifying n3 = 0 Solving n3 = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-5 + -3n + n2)' equal to zero and attempt to solve: Simplifying -5 + -3n + n2 = 0 Solving -5 + -3n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -3n + 5 + n2 = 0 + 5 Reorder the terms: -5 + 5 + -3n + n2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3n + n2 = 0 + 5 -3n + n2 = 0 + 5 Combine like terms: 0 + 5 = 5 -3n + n2 = 5 The n term is -3n. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3n + 2.25 + n2 = 5 + 2.25 Reorder the terms: 2.25 + -3n + n2 = 5 + 2.25 Combine like terms: 5 + 2.25 = 7.25 2.25 + -3n + n2 = 7.25 Factor a perfect square on the left side: (n + -1.5)(n + -1.5) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (n + -1.5) equal to 2.692582404 and -2.692582404.Subproblem 1
n + -1.5 = 2.692582404 Simplifying n + -1.5 = 2.692582404 Reorder the terms: -1.5 + n = 2.692582404 Solving -1.5 + n = 2.692582404 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = 2.692582404 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = 2.692582404 + 1.5 n = 2.692582404 + 1.5 Combine like terms: 2.692582404 + 1.5 = 4.192582404 n = 4.192582404 Simplifying n = 4.192582404Subproblem 2
n + -1.5 = -2.692582404 Simplifying n + -1.5 = -2.692582404 Reorder the terms: -1.5 + n = -2.692582404 Solving -1.5 + n = -2.692582404 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = -2.692582404 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = -2.692582404 + 1.5 n = -2.692582404 + 1.5 Combine like terms: -2.692582404 + 1.5 = -1.192582404 n = -1.192582404 Simplifying n = -1.192582404Solution
The solution to the problem is based on the solutions from the subproblems. n = {4.192582404, -1.192582404}Solution
n = {4.192582404, -1.192582404}
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