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Simplifying 9n2 + -1n + -810 = 0 Reorder the terms: -810 + -1n + 9n2 = 0 Solving -810 + -1n + 9n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -90 + -0.1111111111n + n2 = 0 Move the constant term to the right: Add '90' to each side of the equation. -90 + -0.1111111111n + 90 + n2 = 0 + 90 Reorder the terms: -90 + 90 + -0.1111111111n + n2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + -0.1111111111n + n2 = 0 + 90 -0.1111111111n + n2 = 0 + 90 Combine like terms: 0 + 90 = 90 -0.1111111111n + n2 = 90 The n term is -0.1111111111n. Take half its coefficient (-0.05555555555). Square it (0.003086419752) and add it to both sides. Add '0.003086419752' to each side of the equation. -0.1111111111n + 0.003086419752 + n2 = 90 + 0.003086419752 Reorder the terms: 0.003086419752 + -0.1111111111n + n2 = 90 + 0.003086419752 Combine like terms: 90 + 0.003086419752 = 90.003086419752 0.003086419752 + -0.1111111111n + n2 = 90.003086419752 Factor a perfect square on the left side: (n + -0.05555555555)(n + -0.05555555555) = 90.003086419752 Calculate the square root of the right side: 9.486995648 Break this problem into two subproblems by setting (n + -0.05555555555) equal to 9.486995648 and -9.486995648.Subproblem 1
n + -0.05555555555 = 9.486995648 Simplifying n + -0.05555555555 = 9.486995648 Reorder the terms: -0.05555555555 + n = 9.486995648 Solving -0.05555555555 + n = 9.486995648 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.05555555555' to each side of the equation. -0.05555555555 + 0.05555555555 + n = 9.486995648 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + n = 9.486995648 + 0.05555555555 n = 9.486995648 + 0.05555555555 Combine like terms: 9.486995648 + 0.05555555555 = 9.54255120355 n = 9.54255120355 Simplifying n = 9.54255120355Subproblem 2
n + -0.05555555555 = -9.486995648 Simplifying n + -0.05555555555 = -9.486995648 Reorder the terms: -0.05555555555 + n = -9.486995648 Solving -0.05555555555 + n = -9.486995648 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.05555555555' to each side of the equation. -0.05555555555 + 0.05555555555 + n = -9.486995648 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + n = -9.486995648 + 0.05555555555 n = -9.486995648 + 0.05555555555 Combine like terms: -9.486995648 + 0.05555555555 = -9.43144009245 n = -9.43144009245 Simplifying n = -9.43144009245Solution
The solution to the problem is based on the solutions from the subproblems. n = {9.54255120355, -9.43144009245}
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