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Simplifying 3n2 + -39n + -4 = 0 Reorder the terms: -4 + -39n + 3n2 = 0 Solving -4 + -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'. -1.333333333 + -13n + n2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + -13n + 1.333333333 + n2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + -13n + n2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + -13n + n2 = 0 + 1.333333333 -13n + n2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 -13n + n2 = 1.333333333 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 = 1.333333333 + 42.25 Reorder the terms: 42.25 + -13n + n2 = 1.333333333 + 42.25 Combine like terms: 1.333333333 + 42.25 = 43.583333333 42.25 + -13n + n2 = 43.583333333 Factor a perfect square on the left side: (n + -6.5)(n + -6.5) = 43.583333333 Calculate the square root of the right side: 6.60176744 Break this problem into two subproblems by setting (n + -6.5) equal to 6.60176744 and -6.60176744.Subproblem 1
n + -6.5 = 6.60176744 Simplifying n + -6.5 = 6.60176744 Reorder the terms: -6.5 + n = 6.60176744 Solving -6.5 + n = 6.60176744 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 = 6.60176744 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + n = 6.60176744 + 6.5 n = 6.60176744 + 6.5 Combine like terms: 6.60176744 + 6.5 = 13.10176744 n = 13.10176744 Simplifying n = 13.10176744Subproblem 2
n + -6.5 = -6.60176744 Simplifying n + -6.5 = -6.60176744 Reorder the terms: -6.5 + n = -6.60176744 Solving -6.5 + n = -6.60176744 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 = -6.60176744 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + n = -6.60176744 + 6.5 n = -6.60176744 + 6.5 Combine like terms: -6.60176744 + 6.5 = -0.10176744 n = -0.10176744 Simplifying n = -0.10176744Solution
The solution to the problem is based on the solutions from the subproblems. n = {13.10176744, -0.10176744}
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