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Simplifying 22n + -8 + 5n2 = 0 Reorder the terms: -8 + 22n + 5n2 = 0 Solving -8 + 22n + 5n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.6 + 4.4n + n2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + 4.4n + 1.6 + n2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + 4.4n + n2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + 4.4n + n2 = 0 + 1.6 4.4n + n2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 4.4n + n2 = 1.6 The n term is 4.4n. Take half its coefficient (2.2). Square it (4.84) and add it to both sides. Add '4.84' to each side of the equation. 4.4n + 4.84 + n2 = 1.6 + 4.84 Reorder the terms: 4.84 + 4.4n + n2 = 1.6 + 4.84 Combine like terms: 1.6 + 4.84 = 6.44 4.84 + 4.4n + n2 = 6.44 Factor a perfect square on the left side: (n + 2.2)(n + 2.2) = 6.44 Calculate the square root of the right side: 2.537715508 Break this problem into two subproblems by setting (n + 2.2) equal to 2.537715508 and -2.537715508.Subproblem 1
n + 2.2 = 2.537715508 Simplifying n + 2.2 = 2.537715508 Reorder the terms: 2.2 + n = 2.537715508 Solving 2.2 + n = 2.537715508 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2.2' to each side of the equation. 2.2 + -2.2 + n = 2.537715508 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + n = 2.537715508 + -2.2 n = 2.537715508 + -2.2 Combine like terms: 2.537715508 + -2.2 = 0.337715508 n = 0.337715508 Simplifying n = 0.337715508Subproblem 2
n + 2.2 = -2.537715508 Simplifying n + 2.2 = -2.537715508 Reorder the terms: 2.2 + n = -2.537715508 Solving 2.2 + n = -2.537715508 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2.2' to each side of the equation. 2.2 + -2.2 + n = -2.537715508 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + n = -2.537715508 + -2.2 n = -2.537715508 + -2.2 Combine like terms: -2.537715508 + -2.2 = -4.737715508 n = -4.737715508 Simplifying n = -4.737715508Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.337715508, -4.737715508}
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