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Simplifying 3n3 + -33n2 + 9n = 0 Reorder the terms: 9n + -33n2 + 3n3 = 0 Solving 9n + -33n2 + 3n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3n'. 3n(3 + -11n + n2) = 0 Ignore the factor 3.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 '(3 + -11n + n2)' equal to zero and attempt to solve: Simplifying 3 + -11n + n2 = 0 Solving 3 + -11n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -11n + -3 + n2 = 0 + -3 Reorder the terms: 3 + -3 + -11n + n2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -11n + n2 = 0 + -3 -11n + n2 = 0 + -3 Combine like terms: 0 + -3 = -3 -11n + n2 = -3 The n term is -11n. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11n + 30.25 + n2 = -3 + 30.25 Reorder the terms: 30.25 + -11n + n2 = -3 + 30.25 Combine like terms: -3 + 30.25 = 27.25 30.25 + -11n + n2 = 27.25 Factor a perfect square on the left side: (n + -5.5)(n + -5.5) = 27.25 Calculate the square root of the right side: 5.220153254 Break this problem into two subproblems by setting (n + -5.5) equal to 5.220153254 and -5.220153254.Subproblem 1
n + -5.5 = 5.220153254 Simplifying n + -5.5 = 5.220153254 Reorder the terms: -5.5 + n = 5.220153254 Solving -5.5 + n = 5.220153254 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + n = 5.220153254 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + n = 5.220153254 + 5.5 n = 5.220153254 + 5.5 Combine like terms: 5.220153254 + 5.5 = 10.720153254 n = 10.720153254 Simplifying n = 10.720153254Subproblem 2
n + -5.5 = -5.220153254 Simplifying n + -5.5 = -5.220153254 Reorder the terms: -5.5 + n = -5.220153254 Solving -5.5 + n = -5.220153254 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + n = -5.220153254 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + n = -5.220153254 + 5.5 n = -5.220153254 + 5.5 Combine like terms: -5.220153254 + 5.5 = 0.279846746 n = 0.279846746 Simplifying n = 0.279846746Solution
The solution to the problem is based on the solutions from the subproblems. n = {10.720153254, 0.279846746}Solution
n = {0, 10.720153254, 0.279846746}
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