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Simplifying 3n2 + -1n + -900 = 0 Reorder the terms: -900 + -1n + 3n2 = 0 Solving -900 + -1n + 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'. -300 + -0.3333333333n + n2 = 0 Move the constant term to the right: Add '300' to each side of the equation. -300 + -0.3333333333n + 300 + n2 = 0 + 300 Reorder the terms: -300 + 300 + -0.3333333333n + n2 = 0 + 300 Combine like terms: -300 + 300 = 0 0 + -0.3333333333n + n2 = 0 + 300 -0.3333333333n + n2 = 0 + 300 Combine like terms: 0 + 300 = 300 -0.3333333333n + n2 = 300 The n term is -0.3333333333n. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333n + 0.02777777779 + n2 = 300 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333n + n2 = 300 + 0.02777777779 Combine like terms: 300 + 0.02777777779 = 300.02777777779 0.02777777779 + -0.3333333333n + n2 = 300.02777777779 Factor a perfect square on the left side: (n + -0.1666666667)(n + -0.1666666667) = 300.02777777779 Calculate the square root of the right side: 17.321309933 Break this problem into two subproblems by setting (n + -0.1666666667) equal to 17.321309933 and -17.321309933.Subproblem 1
n + -0.1666666667 = 17.321309933 Simplifying n + -0.1666666667 = 17.321309933 Reorder the terms: -0.1666666667 + n = 17.321309933 Solving -0.1666666667 + n = 17.321309933 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + n = 17.321309933 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + n = 17.321309933 + 0.1666666667 n = 17.321309933 + 0.1666666667 Combine like terms: 17.321309933 + 0.1666666667 = 17.4879765997 n = 17.4879765997 Simplifying n = 17.4879765997Subproblem 2
n + -0.1666666667 = -17.321309933 Simplifying n + -0.1666666667 = -17.321309933 Reorder the terms: -0.1666666667 + n = -17.321309933 Solving -0.1666666667 + n = -17.321309933 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + n = -17.321309933 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + n = -17.321309933 + 0.1666666667 n = -17.321309933 + 0.1666666667 Combine like terms: -17.321309933 + 0.1666666667 = -17.1546432663 n = -17.1546432663 Simplifying n = -17.1546432663Solution
The solution to the problem is based on the solutions from the subproblems. n = {17.4879765997, -17.1546432663}
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