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Simplifying 19n3 + -9n2 + 2n = 0 Reorder the terms: 2n + -9n2 + 19n3 = 0 Solving 2n + -9n2 + 19n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), 'n'. n(2 + -9n + 19n2) = 0Subproblem 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 '(2 + -9n + 19n2)' equal to zero and attempt to solve: Simplifying 2 + -9n + 19n2 = 0 Solving 2 + -9n + 19n2 = 0 Begin completing the square. Divide all terms by 19 the coefficient of the squared term: Divide each side by '19'. 0.1052631579 + -0.4736842105n + n2 = 0 Move the constant term to the right: Add '-0.1052631579' to each side of the equation. 0.1052631579 + -0.4736842105n + -0.1052631579 + n2 = 0 + -0.1052631579 Reorder the terms: 0.1052631579 + -0.1052631579 + -0.4736842105n + n2 = 0 + -0.1052631579 Combine like terms: 0.1052631579 + -0.1052631579 = 0.0000000000 0.0000000000 + -0.4736842105n + n2 = 0 + -0.1052631579 -0.4736842105n + n2 = 0 + -0.1052631579 Combine like terms: 0 + -0.1052631579 = -0.1052631579 -0.4736842105n + n2 = -0.1052631579 The n term is -0.4736842105n. Take half its coefficient (-0.2368421053). Square it (0.05609418284) and add it to both sides. Add '0.05609418284' to each side of the equation. -0.4736842105n + 0.05609418284 + n2 = -0.1052631579 + 0.05609418284 Reorder the terms: 0.05609418284 + -0.4736842105n + n2 = -0.1052631579 + 0.05609418284 Combine like terms: -0.1052631579 + 0.05609418284 = -0.04916897506 0.05609418284 + -0.4736842105n + n2 = -0.04916897506 Factor a perfect square on the left side: (n + -0.2368421053)(n + -0.2368421053) = -0.04916897506 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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