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Simplifying 49n + -35n2 + 49n3 = 0 Solving 49n + -35n2 + 49n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '7n'. 7n(7 + -5n + 7n2) = 0 Ignore the factor 7.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 '(7 + -5n + 7n2)' equal to zero and attempt to solve: Simplifying 7 + -5n + 7n2 = 0 Solving 7 + -5n + 7n2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1 + -0.7142857143n + n2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -0.7142857143n + -1 + n2 = 0 + -1 Reorder the terms: 1 + -1 + -0.7142857143n + n2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -0.7142857143n + n2 = 0 + -1 -0.7142857143n + n2 = 0 + -1 Combine like terms: 0 + -1 = -1 -0.7142857143n + n2 = -1 The n term is -0.7142857143n. Take half its coefficient (-0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. -0.7142857143n + 0.1275510204 + n2 = -1 + 0.1275510204 Reorder the terms: 0.1275510204 + -0.7142857143n + n2 = -1 + 0.1275510204 Combine like terms: -1 + 0.1275510204 = -0.8724489796 0.1275510204 + -0.7142857143n + n2 = -0.8724489796 Factor a perfect square on the left side: (n + -0.3571428572)(n + -0.3571428572) = -0.8724489796 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
n = {0}
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