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Simplifying 2n2 + -10n + 5 = 0 Reorder the terms: 5 + -10n + 2n2 = 0 Solving 5 + -10n + 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'. 2.5 + -5n + n2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -5n + -2.5 + n2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -5n + n2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -5n + n2 = 0 + -2.5 -5n + n2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -5n + n2 = -2.5 The n term is -5n. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5n + 6.25 + n2 = -2.5 + 6.25 Reorder the terms: 6.25 + -5n + n2 = -2.5 + 6.25 Combine like terms: -2.5 + 6.25 = 3.75 6.25 + -5n + n2 = 3.75 Factor a perfect square on the left side: (n + -2.5)(n + -2.5) = 3.75 Calculate the square root of the right side: 1.936491673 Break this problem into two subproblems by setting (n + -2.5) equal to 1.936491673 and -1.936491673.Subproblem 1
n + -2.5 = 1.936491673 Simplifying n + -2.5 = 1.936491673 Reorder the terms: -2.5 + n = 1.936491673 Solving -2.5 + n = 1.936491673 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + n = 1.936491673 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + n = 1.936491673 + 2.5 n = 1.936491673 + 2.5 Combine like terms: 1.936491673 + 2.5 = 4.436491673 n = 4.436491673 Simplifying n = 4.436491673Subproblem 2
n + -2.5 = -1.936491673 Simplifying n + -2.5 = -1.936491673 Reorder the terms: -2.5 + n = -1.936491673 Solving -2.5 + n = -1.936491673 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + n = -1.936491673 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + n = -1.936491673 + 2.5 n = -1.936491673 + 2.5 Combine like terms: -1.936491673 + 2.5 = 0.563508327 n = 0.563508327 Simplifying n = 0.563508327Solution
The solution to the problem is based on the solutions from the subproblems. n = {4.436491673, 0.563508327}
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