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Simplifying 2n3 + -1n2 + -5n = 0 Reorder the terms: -5n + -1n2 + 2n3 = 0 Solving -5n + -1n2 + 2n3 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), 'n'. n(-5 + -1n + 2n2) = 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 '(-5 + -1n + 2n2)' equal to zero and attempt to solve: Simplifying -5 + -1n + 2n2 = 0 Solving -5 + -1n + 2n2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + -0.5n + n2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -0.5n + 2.5 + n2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -0.5n + n2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -0.5n + n2 = 0 + 2.5 -0.5n + n2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -0.5n + n2 = 2.5 The n term is -0.5n. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5n + 0.0625 + n2 = 2.5 + 0.0625 Reorder the terms: 0.0625 + -0.5n + n2 = 2.5 + 0.0625 Combine like terms: 2.5 + 0.0625 = 2.5625 0.0625 + -0.5n + n2 = 2.5625 Factor a perfect square on the left side: (n + -0.25)(n + -0.25) = 2.5625 Calculate the square root of the right side: 1.600781059 Break this problem into two subproblems by setting (n + -0.25) equal to 1.600781059 and -1.600781059.Subproblem 1
n + -0.25 = 1.600781059 Simplifying n + -0.25 = 1.600781059 Reorder the terms: -0.25 + n = 1.600781059 Solving -0.25 + n = 1.600781059 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + n = 1.600781059 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + n = 1.600781059 + 0.25 n = 1.600781059 + 0.25 Combine like terms: 1.600781059 + 0.25 = 1.850781059 n = 1.850781059 Simplifying n = 1.850781059Subproblem 2
n + -0.25 = -1.600781059 Simplifying n + -0.25 = -1.600781059 Reorder the terms: -0.25 + n = -1.600781059 Solving -0.25 + n = -1.600781059 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + n = -1.600781059 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + n = -1.600781059 + 0.25 n = -1.600781059 + 0.25 Combine like terms: -1.600781059 + 0.25 = -1.350781059 n = -1.350781059 Simplifying n = -1.350781059Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.850781059, -1.350781059}Solution
n = {0, 1.850781059, -1.350781059}
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