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Simplifying 6n2 + 39n + -8 = 0 Reorder the terms: -8 + 39n + 6n2 = 0 Solving -8 + 39n + 6n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.333333333 + 6.5n + n2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + 6.5n + 1.333333333 + n2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + 6.5n + n2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + 6.5n + n2 = 0 + 1.333333333 6.5n + n2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 6.5n + n2 = 1.333333333 The n term is 6.5n. Take half its coefficient (3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. 6.5n + 10.5625 + n2 = 1.333333333 + 10.5625 Reorder the terms: 10.5625 + 6.5n + n2 = 1.333333333 + 10.5625 Combine like terms: 1.333333333 + 10.5625 = 11.895833333 10.5625 + 6.5n + n2 = 11.895833333 Factor a perfect square on the left side: (n + 3.25)(n + 3.25) = 11.895833333 Calculate the square root of the right side: 3.449033681 Break this problem into two subproblems by setting (n + 3.25) equal to 3.449033681 and -3.449033681.Subproblem 1
n + 3.25 = 3.449033681 Simplifying n + 3.25 = 3.449033681 Reorder the terms: 3.25 + n = 3.449033681 Solving 3.25 + n = 3.449033681 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + n = 3.449033681 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + n = 3.449033681 + -3.25 n = 3.449033681 + -3.25 Combine like terms: 3.449033681 + -3.25 = 0.199033681 n = 0.199033681 Simplifying n = 0.199033681Subproblem 2
n + 3.25 = -3.449033681 Simplifying n + 3.25 = -3.449033681 Reorder the terms: 3.25 + n = -3.449033681 Solving 3.25 + n = -3.449033681 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + n = -3.449033681 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + n = -3.449033681 + -3.25 n = -3.449033681 + -3.25 Combine like terms: -3.449033681 + -3.25 = -6.699033681 n = -6.699033681 Simplifying n = -6.699033681Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.199033681, -6.699033681}
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