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Simplifying (2n2) + -5n = 1 Reorder the terms: -5n + (2n2) = 1 Solving -5n + (2n2) = 1 Solving for variable 'n'. Reorder the terms: -1 + -5n + (2n2) = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -5n + (2n2) = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + -2.5n + n2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -2.5n + 0.5 + n2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -2.5n + n2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -2.5n + n2 = 0 + 0.5 -2.5n + n2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -2.5n + n2 = 0.5 The n term is -2.5n. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5n + 1.5625 + n2 = 0.5 + 1.5625 Reorder the terms: 1.5625 + -2.5n + n2 = 0.5 + 1.5625 Combine like terms: 0.5 + 1.5625 = 2.0625 1.5625 + -2.5n + n2 = 2.0625 Factor a perfect square on the left side: ((n) + -1.25)((n) + -1.25) = 2.0625 Calculate the square root of the right side: 1.436140662 Break this problem into two subproblems by setting ((n) + -1.25) equal to 1.436140662 and -1.436140662.Subproblem 1
(n) + -1.25 = 1.436140662 Simplifying (n) + -1.25 = 1.436140662 n + -1.25 = 1.436140662 Reorder the terms: -1.25 + n = 1.436140662 Solving -1.25 + n = 1.436140662 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + n = 1.436140662 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + n = 1.436140662 + 1.25 n = 1.436140662 + 1.25 Combine like terms: 1.436140662 + 1.25 = 2.686140662 n = 2.686140662 Simplifying n = 2.686140662Subproblem 2
(n) + -1.25 = -1.436140662 Simplifying (n) + -1.25 = -1.436140662 n + -1.25 = -1.436140662 Reorder the terms: -1.25 + n = -1.436140662 Solving -1.25 + n = -1.436140662 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + n = -1.436140662 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + n = -1.436140662 + 1.25 n = -1.436140662 + 1.25 Combine like terms: -1.436140662 + 1.25 = -0.186140662 n = -0.186140662 Simplifying n = -0.186140662Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.686140662, -0.186140662}
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