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Simplifying 3n2 + -39n + -2 = 0 Reorder the terms: -2 + -39n + 3n2 = 0 Solving -2 + -39n + 3n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.6666666667 + -13n + n2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -13n + 0.6666666667 + n2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -13n + n2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -13n + n2 = 0 + 0.6666666667 -13n + n2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -13n + n2 = 0.6666666667 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 = 0.6666666667 + 42.25 Reorder the terms: 42.25 + -13n + n2 = 0.6666666667 + 42.25 Combine like terms: 0.6666666667 + 42.25 = 42.9166666667 42.25 + -13n + n2 = 42.9166666667 Factor a perfect square on the left side: (n + -6.5)(n + -6.5) = 42.9166666667 Calculate the square root of the right side: 6.551081336 Break this problem into two subproblems by setting (n + -6.5) equal to 6.551081336 and -6.551081336.Subproblem 1
n + -6.5 = 6.551081336 Simplifying n + -6.5 = 6.551081336 Reorder the terms: -6.5 + n = 6.551081336 Solving -6.5 + n = 6.551081336 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 = 6.551081336 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + n = 6.551081336 + 6.5 n = 6.551081336 + 6.5 Combine like terms: 6.551081336 + 6.5 = 13.051081336 n = 13.051081336 Simplifying n = 13.051081336Subproblem 2
n + -6.5 = -6.551081336 Simplifying n + -6.5 = -6.551081336 Reorder the terms: -6.5 + n = -6.551081336 Solving -6.5 + n = -6.551081336 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 = -6.551081336 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + n = -6.551081336 + 6.5 n = -6.551081336 + 6.5 Combine like terms: -6.551081336 + 6.5 = -0.051081336 n = -0.051081336 Simplifying n = -0.051081336Solution
The solution to the problem is based on the solutions from the subproblems. n = {13.051081336, -0.051081336}
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