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Simplifying 2n3 + -24n2 + -23048n = 0 Reorder the terms: -23048n + -24n2 + 2n3 = 0 Solving -23048n + -24n2 + 2n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2n'. 2n(-11524 + -12n + n2) = 0 Ignore the factor 2.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 '(-11524 + -12n + n2)' equal to zero and attempt to solve: Simplifying -11524 + -12n + n2 = 0 Solving -11524 + -12n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '11524' to each side of the equation. -11524 + -12n + 11524 + n2 = 0 + 11524 Reorder the terms: -11524 + 11524 + -12n + n2 = 0 + 11524 Combine like terms: -11524 + 11524 = 0 0 + -12n + n2 = 0 + 11524 -12n + n2 = 0 + 11524 Combine like terms: 0 + 11524 = 11524 -12n + n2 = 11524 The n term is -12n. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12n + 36 + n2 = 11524 + 36 Reorder the terms: 36 + -12n + n2 = 11524 + 36 Combine like terms: 11524 + 36 = 11560 36 + -12n + n2 = 11560 Factor a perfect square on the left side: (n + -6)(n + -6) = 11560 Calculate the square root of the right side: 107.517440446 Break this problem into two subproblems by setting (n + -6) equal to 107.517440446 and -107.517440446.Subproblem 1
n + -6 = 107.517440446 Simplifying n + -6 = 107.517440446 Reorder the terms: -6 + n = 107.517440446 Solving -6 + n = 107.517440446 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + n = 107.517440446 + 6 Combine like terms: -6 + 6 = 0 0 + n = 107.517440446 + 6 n = 107.517440446 + 6 Combine like terms: 107.517440446 + 6 = 113.517440446 n = 113.517440446 Simplifying n = 113.517440446Subproblem 2
n + -6 = -107.517440446 Simplifying n + -6 = -107.517440446 Reorder the terms: -6 + n = -107.517440446 Solving -6 + n = -107.517440446 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + n = -107.517440446 + 6 Combine like terms: -6 + 6 = 0 0 + n = -107.517440446 + 6 n = -107.517440446 + 6 Combine like terms: -107.517440446 + 6 = -101.517440446 n = -101.517440446 Simplifying n = -101.517440446Solution
The solution to the problem is based on the solutions from the subproblems. n = {113.517440446, -101.517440446}Solution
n = {0, 113.517440446, -101.517440446}
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