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Simplifying 2n2 + -18n + -35 = 0 Reorder the terms: -35 + -18n + 2n2 = 0 Solving -35 + -18n + 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'. -17.5 + -9n + n2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + -9n + 17.5 + n2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + -9n + n2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + -9n + n2 = 0 + 17.5 -9n + n2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 -9n + n2 = 17.5 The n term is -9n. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9n + 20.25 + n2 = 17.5 + 20.25 Reorder the terms: 20.25 + -9n + n2 = 17.5 + 20.25 Combine like terms: 17.5 + 20.25 = 37.75 20.25 + -9n + n2 = 37.75 Factor a perfect square on the left side: (n + -4.5)(n + -4.5) = 37.75 Calculate the square root of the right side: 6.144102864 Break this problem into two subproblems by setting (n + -4.5) equal to 6.144102864 and -6.144102864.Subproblem 1
n + -4.5 = 6.144102864 Simplifying n + -4.5 = 6.144102864 Reorder the terms: -4.5 + n = 6.144102864 Solving -4.5 + n = 6.144102864 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + n = 6.144102864 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + n = 6.144102864 + 4.5 n = 6.144102864 + 4.5 Combine like terms: 6.144102864 + 4.5 = 10.644102864 n = 10.644102864 Simplifying n = 10.644102864Subproblem 2
n + -4.5 = -6.144102864 Simplifying n + -4.5 = -6.144102864 Reorder the terms: -4.5 + n = -6.144102864 Solving -4.5 + n = -6.144102864 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + n = -6.144102864 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + n = -6.144102864 + 4.5 n = -6.144102864 + 4.5 Combine like terms: -6.144102864 + 4.5 = -1.644102864 n = -1.644102864 Simplifying n = -1.644102864Solution
The solution to the problem is based on the solutions from the subproblems. n = {10.644102864, -1.644102864}
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