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Simplifying 3n3 + -12n2 + -30n = 0 Reorder the terms: -30n + -12n2 + 3n3 = 0 Solving -30n + -12n2 + 3n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3n'. 3n(-10 + -4n + 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 '(-10 + -4n + n2)' equal to zero and attempt to solve: Simplifying -10 + -4n + n2 = 0 Solving -10 + -4n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -4n + 10 + n2 = 0 + 10 Reorder the terms: -10 + 10 + -4n + n2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -4n + n2 = 0 + 10 -4n + n2 = 0 + 10 Combine like terms: 0 + 10 = 10 -4n + n2 = 10 The n term is -4n. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4n + 4 + n2 = 10 + 4 Reorder the terms: 4 + -4n + n2 = 10 + 4 Combine like terms: 10 + 4 = 14 4 + -4n + n2 = 14 Factor a perfect square on the left side: (n + -2)(n + -2) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (n + -2) equal to 3.741657387 and -3.741657387.Subproblem 1
n + -2 = 3.741657387 Simplifying n + -2 = 3.741657387 Reorder the terms: -2 + n = 3.741657387 Solving -2 + n = 3.741657387 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + n = 3.741657387 + 2 Combine like terms: -2 + 2 = 0 0 + n = 3.741657387 + 2 n = 3.741657387 + 2 Combine like terms: 3.741657387 + 2 = 5.741657387 n = 5.741657387 Simplifying n = 5.741657387Subproblem 2
n + -2 = -3.741657387 Simplifying n + -2 = -3.741657387 Reorder the terms: -2 + n = -3.741657387 Solving -2 + n = -3.741657387 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + n = -3.741657387 + 2 Combine like terms: -2 + 2 = 0 0 + n = -3.741657387 + 2 n = -3.741657387 + 2 Combine like terms: -3.741657387 + 2 = -1.741657387 n = -1.741657387 Simplifying n = -1.741657387Solution
The solution to the problem is based on the solutions from the subproblems. n = {5.741657387, -1.741657387}Solution
n = {0, 5.741657387, -1.741657387}
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