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Simplifying 2n2 + 6n + -35 = 0 Reorder the terms: -35 + 6n + 2n2 = 0 Solving -35 + 6n + 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 + 3n + n2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + 3n + 17.5 + n2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + 3n + n2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + 3n + n2 = 0 + 17.5 3n + n2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 3n + n2 = 17.5 The n term is 3n. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3n + 2.25 + n2 = 17.5 + 2.25 Reorder the terms: 2.25 + 3n + n2 = 17.5 + 2.25 Combine like terms: 17.5 + 2.25 = 19.75 2.25 + 3n + n2 = 19.75 Factor a perfect square on the left side: (n + 1.5)(n + 1.5) = 19.75 Calculate the square root of the right side: 4.444097209 Break this problem into two subproblems by setting (n + 1.5) equal to 4.444097209 and -4.444097209.Subproblem 1
n + 1.5 = 4.444097209 Simplifying n + 1.5 = 4.444097209 Reorder the terms: 1.5 + n = 4.444097209 Solving 1.5 + n = 4.444097209 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + n = 4.444097209 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + n = 4.444097209 + -1.5 n = 4.444097209 + -1.5 Combine like terms: 4.444097209 + -1.5 = 2.944097209 n = 2.944097209 Simplifying n = 2.944097209Subproblem 2
n + 1.5 = -4.444097209 Simplifying n + 1.5 = -4.444097209 Reorder the terms: 1.5 + n = -4.444097209 Solving 1.5 + n = -4.444097209 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + n = -4.444097209 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + n = -4.444097209 + -1.5 n = -4.444097209 + -1.5 Combine like terms: -4.444097209 + -1.5 = -5.944097209 n = -5.944097209 Simplifying n = -5.944097209Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.944097209, -5.944097209}
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