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Simplifying (9n * n) = 4 + 7n Multiply n * n (9n2) = 4 + 7n Solving (9n2) = 4 + 7n Solving for variable 'n'. Reorder the terms: -4 + -7n + (9n2) = 4 + 7n + -4 + -7n Reorder the terms: -4 + -7n + (9n2) = 4 + -4 + 7n + -7n Combine like terms: 4 + -4 = 0 -4 + -7n + (9n2) = 0 + 7n + -7n -4 + -7n + (9n2) = 7n + -7n Combine like terms: 7n + -7n = 0 -4 + -7n + (9n2) = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.4444444444 + -0.7777777778n + n2 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + -0.7777777778n + 0.4444444444 + n2 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + -0.7777777778n + n2 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + -0.7777777778n + n2 = 0 + 0.4444444444 -0.7777777778n + n2 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 -0.7777777778n + n2 = 0.4444444444 The n term is -0.7777777778n. Take half its coefficient (-0.3888888889). Square it (0.1512345679) and add it to both sides. Add '0.1512345679' to each side of the equation. -0.7777777778n + 0.1512345679 + n2 = 0.4444444444 + 0.1512345679 Reorder the terms: 0.1512345679 + -0.7777777778n + n2 = 0.4444444444 + 0.1512345679 Combine like terms: 0.4444444444 + 0.1512345679 = 0.5956790123 0.1512345679 + -0.7777777778n + n2 = 0.5956790123 Factor a perfect square on the left side: ((n) + -0.3888888889)((n) + -0.3888888889) = 0.5956790123 Calculate the square root of the right side: 0.771802444 Break this problem into two subproblems by setting ((n) + -0.3888888889) equal to 0.771802444 and -0.771802444.Subproblem 1
(n) + -0.3888888889 = 0.771802444 Simplifying (n) + -0.3888888889 = 0.771802444 n + -0.3888888889 = 0.771802444 Reorder the terms: -0.3888888889 + n = 0.771802444 Solving -0.3888888889 + n = 0.771802444 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.3888888889' to each side of the equation. -0.3888888889 + 0.3888888889 + n = 0.771802444 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + n = 0.771802444 + 0.3888888889 n = 0.771802444 + 0.3888888889 Combine like terms: 0.771802444 + 0.3888888889 = 1.1606913329 n = 1.1606913329 Simplifying n = 1.1606913329Subproblem 2
(n) + -0.3888888889 = -0.771802444 Simplifying (n) + -0.3888888889 = -0.771802444 n + -0.3888888889 = -0.771802444 Reorder the terms: -0.3888888889 + n = -0.771802444 Solving -0.3888888889 + n = -0.771802444 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.3888888889' to each side of the equation. -0.3888888889 + 0.3888888889 + n = -0.771802444 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + n = -0.771802444 + 0.3888888889 n = -0.771802444 + 0.3888888889 Combine like terms: -0.771802444 + 0.3888888889 = -0.3829135551 n = -0.3829135551 Simplifying n = -0.3829135551Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.1606913329, -0.3829135551}
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