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Simplifying 9n3 + 18n2 + -121n = 0 Reorder the terms: -121n + 18n2 + 9n3 = 0 Solving -121n + 18n2 + 9n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), 'n'. n(-121 + 18n + 9n2) = 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 '(-121 + 18n + 9n2)' equal to zero and attempt to solve: Simplifying -121 + 18n + 9n2 = 0 Solving -121 + 18n + 9n2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -13.44444444 + 2n + n2 = 0 Move the constant term to the right: Add '13.44444444' to each side of the equation. -13.44444444 + 2n + 13.44444444 + n2 = 0 + 13.44444444 Reorder the terms: -13.44444444 + 13.44444444 + 2n + n2 = 0 + 13.44444444 Combine like terms: -13.44444444 + 13.44444444 = 0.00000000 0.00000000 + 2n + n2 = 0 + 13.44444444 2n + n2 = 0 + 13.44444444 Combine like terms: 0 + 13.44444444 = 13.44444444 2n + n2 = 13.44444444 The n term is 2n. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2n + 1 + n2 = 13.44444444 + 1 Reorder the terms: 1 + 2n + n2 = 13.44444444 + 1 Combine like terms: 13.44444444 + 1 = 14.44444444 1 + 2n + n2 = 14.44444444 Factor a perfect square on the left side: (n + 1)(n + 1) = 14.44444444 Calculate the square root of the right side: 3.80058475 Break this problem into two subproblems by setting (n + 1) equal to 3.80058475 and -3.80058475.Subproblem 1
n + 1 = 3.80058475 Simplifying n + 1 = 3.80058475 Reorder the terms: 1 + n = 3.80058475 Solving 1 + n = 3.80058475 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + n = 3.80058475 + -1 Combine like terms: 1 + -1 = 0 0 + n = 3.80058475 + -1 n = 3.80058475 + -1 Combine like terms: 3.80058475 + -1 = 2.80058475 n = 2.80058475 Simplifying n = 2.80058475Subproblem 2
n + 1 = -3.80058475 Simplifying n + 1 = -3.80058475 Reorder the terms: 1 + n = -3.80058475 Solving 1 + n = -3.80058475 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + n = -3.80058475 + -1 Combine like terms: 1 + -1 = 0 0 + n = -3.80058475 + -1 n = -3.80058475 + -1 Combine like terms: -3.80058475 + -1 = -4.80058475 n = -4.80058475 Simplifying n = -4.80058475Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.80058475, -4.80058475}Solution
n = {0, 2.80058475, -4.80058475}
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