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Simplifying 3n2 + 2n + -3900 = 0 Reorder the terms: -3900 + 2n + 3n2 = 0 Solving -3900 + 2n + 3n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1300 + 0.6666666667n + n2 = 0 Move the constant term to the right: Add '1300' to each side of the equation. -1300 + 0.6666666667n + 1300 + n2 = 0 + 1300 Reorder the terms: -1300 + 1300 + 0.6666666667n + n2 = 0 + 1300 Combine like terms: -1300 + 1300 = 0 0 + 0.6666666667n + n2 = 0 + 1300 0.6666666667n + n2 = 0 + 1300 Combine like terms: 0 + 1300 = 1300 0.6666666667n + n2 = 1300 The n term is 0.6666666667n. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667n + 0.1111111112 + n2 = 1300 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667n + n2 = 1300 + 0.1111111112 Combine like terms: 1300 + 0.1111111112 = 1300.1111111112 0.1111111112 + 0.6666666667n + n2 = 1300.1111111112 Factor a perfect square on the left side: (n + 0.3333333334)(n + 0.3333333334) = 1300.1111111112 Calculate the square root of the right side: 36.057053556 Break this problem into two subproblems by setting (n + 0.3333333334) equal to 36.057053556 and -36.057053556.Subproblem 1
n + 0.3333333334 = 36.057053556 Simplifying n + 0.3333333334 = 36.057053556 Reorder the terms: 0.3333333334 + n = 36.057053556 Solving 0.3333333334 + n = 36.057053556 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + n = 36.057053556 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + n = 36.057053556 + -0.3333333334 n = 36.057053556 + -0.3333333334 Combine like terms: 36.057053556 + -0.3333333334 = 35.7237202226 n = 35.7237202226 Simplifying n = 35.7237202226Subproblem 2
n + 0.3333333334 = -36.057053556 Simplifying n + 0.3333333334 = -36.057053556 Reorder the terms: 0.3333333334 + n = -36.057053556 Solving 0.3333333334 + n = -36.057053556 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + n = -36.057053556 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + n = -36.057053556 + -0.3333333334 n = -36.057053556 + -0.3333333334 Combine like terms: -36.057053556 + -0.3333333334 = -36.3903868894 n = -36.3903868894 Simplifying n = -36.3903868894Solution
The solution to the problem is based on the solutions from the subproblems. n = {35.7237202226, -36.3903868894}
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