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Simplifying 2n2 + -13n + -35 = 0 Reorder the terms: -35 + -13n + 2n2 = 0 Solving -35 + -13n + 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 + -6.5n + n2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + -6.5n + 17.5 + n2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + -6.5n + n2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + -6.5n + n2 = 0 + 17.5 -6.5n + n2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 -6.5n + n2 = 17.5 The n term is -6.5n. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5n + 10.5625 + n2 = 17.5 + 10.5625 Reorder the terms: 10.5625 + -6.5n + n2 = 17.5 + 10.5625 Combine like terms: 17.5 + 10.5625 = 28.0625 10.5625 + -6.5n + n2 = 28.0625 Factor a perfect square on the left side: (n + -3.25)(n + -3.25) = 28.0625 Calculate the square root of the right side: 5.297405025 Break this problem into two subproblems by setting (n + -3.25) equal to 5.297405025 and -5.297405025.Subproblem 1
n + -3.25 = 5.297405025 Simplifying n + -3.25 = 5.297405025 Reorder the terms: -3.25 + n = 5.297405025 Solving -3.25 + n = 5.297405025 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + n = 5.297405025 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + n = 5.297405025 + 3.25 n = 5.297405025 + 3.25 Combine like terms: 5.297405025 + 3.25 = 8.547405025 n = 8.547405025 Simplifying n = 8.547405025Subproblem 2
n + -3.25 = -5.297405025 Simplifying n + -3.25 = -5.297405025 Reorder the terms: -3.25 + n = -5.297405025 Solving -3.25 + n = -5.297405025 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + n = -5.297405025 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + n = -5.297405025 + 3.25 n = -5.297405025 + 3.25 Combine like terms: -5.297405025 + 3.25 = -2.047405025 n = -2.047405025 Simplifying n = -2.047405025Solution
The solution to the problem is based on the solutions from the subproblems. n = {8.547405025, -2.047405025}
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