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Simplifying 9n2 + -7n + -21 = 0 Reorder the terms: -21 + -7n + 9n2 = 0 Solving -21 + -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'. -2.333333333 + -0.7777777778n + n2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + -0.7777777778n + 2.333333333 + n2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + -0.7777777778n + n2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + -0.7777777778n + n2 = 0 + 2.333333333 -0.7777777778n + n2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 -0.7777777778n + n2 = 2.333333333 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 = 2.333333333 + 0.1512345679 Reorder the terms: 0.1512345679 + -0.7777777778n + n2 = 2.333333333 + 0.1512345679 Combine like terms: 2.333333333 + 0.1512345679 = 2.4845679009 0.1512345679 + -0.7777777778n + n2 = 2.4845679009 Factor a perfect square on the left side: (n + -0.3888888889)(n + -0.3888888889) = 2.4845679009 Calculate the square root of the right side: 1.576251218 Break this problem into two subproblems by setting (n + -0.3888888889) equal to 1.576251218 and -1.576251218.Subproblem 1
n + -0.3888888889 = 1.576251218 Simplifying n + -0.3888888889 = 1.576251218 Reorder the terms: -0.3888888889 + n = 1.576251218 Solving -0.3888888889 + n = 1.576251218 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 = 1.576251218 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + n = 1.576251218 + 0.3888888889 n = 1.576251218 + 0.3888888889 Combine like terms: 1.576251218 + 0.3888888889 = 1.9651401069 n = 1.9651401069 Simplifying n = 1.9651401069Subproblem 2
n + -0.3888888889 = -1.576251218 Simplifying n + -0.3888888889 = -1.576251218 Reorder the terms: -0.3888888889 + n = -1.576251218 Solving -0.3888888889 + n = -1.576251218 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 = -1.576251218 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + n = -1.576251218 + 0.3888888889 n = -1.576251218 + 0.3888888889 Combine like terms: -1.576251218 + 0.3888888889 = -1.1873623291 n = -1.1873623291 Simplifying n = -1.1873623291Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.9651401069, -1.1873623291}
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