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Simplifying 2n2 + 20n + -191 = 0 Reorder the terms: -191 + 20n + 2n2 = 0 Solving -191 + 20n + 2n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -95.5 + 10n + n2 = 0 Move the constant term to the right: Add '95.5' to each side of the equation. -95.5 + 10n + 95.5 + n2 = 0 + 95.5 Reorder the terms: -95.5 + 95.5 + 10n + n2 = 0 + 95.5 Combine like terms: -95.5 + 95.5 = 0.0 0.0 + 10n + n2 = 0 + 95.5 10n + n2 = 0 + 95.5 Combine like terms: 0 + 95.5 = 95.5 10n + n2 = 95.5 The n term is 10n. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10n + 25 + n2 = 95.5 + 25 Reorder the terms: 25 + 10n + n2 = 95.5 + 25 Combine like terms: 95.5 + 25 = 120.5 25 + 10n + n2 = 120.5 Factor a perfect square on the left side: (n + 5)(n + 5) = 120.5 Calculate the square root of the right side: 10.9772492 Break this problem into two subproblems by setting (n + 5) equal to 10.9772492 and -10.9772492.Subproblem 1
n + 5 = 10.9772492 Simplifying n + 5 = 10.9772492 Reorder the terms: 5 + n = 10.9772492 Solving 5 + n = 10.9772492 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + n = 10.9772492 + -5 Combine like terms: 5 + -5 = 0 0 + n = 10.9772492 + -5 n = 10.9772492 + -5 Combine like terms: 10.9772492 + -5 = 5.9772492 n = 5.9772492 Simplifying n = 5.9772492Subproblem 2
n + 5 = -10.9772492 Simplifying n + 5 = -10.9772492 Reorder the terms: 5 + n = -10.9772492 Solving 5 + n = -10.9772492 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + n = -10.9772492 + -5 Combine like terms: 5 + -5 = 0 0 + n = -10.9772492 + -5 n = -10.9772492 + -5 Combine like terms: -10.9772492 + -5 = -15.9772492 n = -15.9772492 Simplifying n = -15.9772492Solution
The solution to the problem is based on the solutions from the subproblems. n = {5.9772492, -15.9772492}
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