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Simplifying 9n2 + -7n + -5 = 0 Reorder the terms: -5 + -7n + 9n2 = 0 Solving -5 + -7n + 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'. -0.5555555556 + -0.7777777778n + n2 = 0 Move the constant term to the right: Add '0.5555555556' to each side of the equation. -0.5555555556 + -0.7777777778n + 0.5555555556 + n2 = 0 + 0.5555555556 Reorder the terms: -0.5555555556 + 0.5555555556 + -0.7777777778n + n2 = 0 + 0.5555555556 Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000 0.0000000000 + -0.7777777778n + n2 = 0 + 0.5555555556 -0.7777777778n + n2 = 0 + 0.5555555556 Combine like terms: 0 + 0.5555555556 = 0.5555555556 -0.7777777778n + n2 = 0.5555555556 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 = 0.5555555556 + 0.1512345679 Reorder the terms: 0.1512345679 + -0.7777777778n + n2 = 0.5555555556 + 0.1512345679 Combine like terms: 0.5555555556 + 0.1512345679 = 0.7067901235 0.1512345679 + -0.7777777778n + n2 = 0.7067901235 Factor a perfect square on the left side: (n + -0.3888888889)(n + -0.3888888889) = 0.7067901235 Calculate the square root of the right side: 0.840708108 Break this problem into two subproblems by setting (n + -0.3888888889) equal to 0.840708108 and -0.840708108.Subproblem 1
n + -0.3888888889 = 0.840708108 Simplifying n + -0.3888888889 = 0.840708108 Reorder the terms: -0.3888888889 + n = 0.840708108 Solving -0.3888888889 + n = 0.840708108 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 = 0.840708108 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + n = 0.840708108 + 0.3888888889 n = 0.840708108 + 0.3888888889 Combine like terms: 0.840708108 + 0.3888888889 = 1.2295969969 n = 1.2295969969 Simplifying n = 1.2295969969Subproblem 2
n + -0.3888888889 = -0.840708108 Simplifying n + -0.3888888889 = -0.840708108 Reorder the terms: -0.3888888889 + n = -0.840708108 Solving -0.3888888889 + n = -0.840708108 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 = -0.840708108 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + n = -0.840708108 + 0.3888888889 n = -0.840708108 + 0.3888888889 Combine like terms: -0.840708108 + 0.3888888889 = -0.4518192191 n = -0.4518192191 Simplifying n = -0.4518192191Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.2295969969, -0.4518192191}
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