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Simplifying 13n3 + -1n2 + n4 + 3n2 + -9n2 = 0 Reorder the terms: -1n2 + 3n2 + -9n2 + 13n3 + n4 = 0 Combine like terms: -1n2 + 3n2 = 2n2 2n2 + -9n2 + 13n3 + n4 = 0 Combine like terms: 2n2 + -9n2 = -7n2 -7n2 + 13n3 + n4 = 0 Solving -7n2 + 13n3 + n4 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), 'n2'. n2(-7 + 13n + n2) = 0Subproblem 1
Set the factor 'n2' equal to zero and attempt to solve: Simplifying n2 = 0 Solving n2 = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n2 = 0 Take the square root of each side: n = {0}Subproblem 2
Set the factor '(-7 + 13n + n2)' equal to zero and attempt to solve: Simplifying -7 + 13n + n2 = 0 Solving -7 + 13n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 13n + 7 + n2 = 0 + 7 Reorder the terms: -7 + 7 + 13n + n2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 13n + n2 = 0 + 7 13n + n2 = 0 + 7 Combine like terms: 0 + 7 = 7 13n + n2 = 7 The n term is 13n. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13n + 42.25 + n2 = 7 + 42.25 Reorder the terms: 42.25 + 13n + n2 = 7 + 42.25 Combine like terms: 7 + 42.25 = 49.25 42.25 + 13n + n2 = 49.25 Factor a perfect square on the left side: (n + 6.5)(n + 6.5) = 49.25 Calculate the square root of the right side: 7.017834424 Break this problem into two subproblems by setting (n + 6.5) equal to 7.017834424 and -7.017834424.Subproblem 1
n + 6.5 = 7.017834424 Simplifying n + 6.5 = 7.017834424 Reorder the terms: 6.5 + n = 7.017834424 Solving 6.5 + n = 7.017834424 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + n = 7.017834424 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + n = 7.017834424 + -6.5 n = 7.017834424 + -6.5 Combine like terms: 7.017834424 + -6.5 = 0.517834424 n = 0.517834424 Simplifying n = 0.517834424Subproblem 2
n + 6.5 = -7.017834424 Simplifying n + 6.5 = -7.017834424 Reorder the terms: 6.5 + n = -7.017834424 Solving 6.5 + n = -7.017834424 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + n = -7.017834424 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + n = -7.017834424 + -6.5 n = -7.017834424 + -6.5 Combine like terms: -7.017834424 + -6.5 = -13.517834424 n = -13.517834424 Simplifying n = -13.517834424Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.517834424, -13.517834424}Solution
n = {0, 0.517834424, -13.517834424}
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