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Simplifying 10n2 + -65n + -36 = 0 Reorder the terms: -36 + -65n + 10n2 = 0 Solving -36 + -65n + 10n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -3.6 + -6.5n + n2 = 0 Move the constant term to the right: Add '3.6' to each side of the equation. -3.6 + -6.5n + 3.6 + n2 = 0 + 3.6 Reorder the terms: -3.6 + 3.6 + -6.5n + n2 = 0 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + -6.5n + n2 = 0 + 3.6 -6.5n + n2 = 0 + 3.6 Combine like terms: 0 + 3.6 = 3.6 -6.5n + n2 = 3.6 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 = 3.6 + 10.5625 Reorder the terms: 10.5625 + -6.5n + n2 = 3.6 + 10.5625 Combine like terms: 3.6 + 10.5625 = 14.1625 10.5625 + -6.5n + n2 = 14.1625 Factor a perfect square on the left side: (n + -3.25)(n + -3.25) = 14.1625 Calculate the square root of the right side: 3.763309714 Break this problem into two subproblems by setting (n + -3.25) equal to 3.763309714 and -3.763309714.Subproblem 1
n + -3.25 = 3.763309714 Simplifying n + -3.25 = 3.763309714 Reorder the terms: -3.25 + n = 3.763309714 Solving -3.25 + n = 3.763309714 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 = 3.763309714 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + n = 3.763309714 + 3.25 n = 3.763309714 + 3.25 Combine like terms: 3.763309714 + 3.25 = 7.013309714 n = 7.013309714 Simplifying n = 7.013309714Subproblem 2
n + -3.25 = -3.763309714 Simplifying n + -3.25 = -3.763309714 Reorder the terms: -3.25 + n = -3.763309714 Solving -3.25 + n = -3.763309714 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 = -3.763309714 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + n = -3.763309714 + 3.25 n = -3.763309714 + 3.25 Combine like terms: -3.763309714 + 3.25 = -0.513309714 n = -0.513309714 Simplifying n = -0.513309714Solution
The solution to the problem is based on the solutions from the subproblems. n = {7.013309714, -0.513309714}
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