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Simplifying 9n2 + -2n + -2 = 0 Reorder the terms: -2 + -2n + 9n2 = 0 Solving -2 + -2n + 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'. -0.2222222222 + -0.2222222222n + n2 = 0 Move the constant term to the right: Add '0.2222222222' to each side of the equation. -0.2222222222 + -0.2222222222n + 0.2222222222 + n2 = 0 + 0.2222222222 Reorder the terms: -0.2222222222 + 0.2222222222 + -0.2222222222n + n2 = 0 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + -0.2222222222n + n2 = 0 + 0.2222222222 -0.2222222222n + n2 = 0 + 0.2222222222 Combine like terms: 0 + 0.2222222222 = 0.2222222222 -0.2222222222n + n2 = 0.2222222222 The n term is -0.2222222222n. Take half its coefficient (-0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. -0.2222222222n + 0.01234567901 + n2 = 0.2222222222 + 0.01234567901 Reorder the terms: 0.01234567901 + -0.2222222222n + n2 = 0.2222222222 + 0.01234567901 Combine like terms: 0.2222222222 + 0.01234567901 = 0.23456790121 0.01234567901 + -0.2222222222n + n2 = 0.23456790121 Factor a perfect square on the left side: (n + -0.1111111111)(n + -0.1111111111) = 0.23456790121 Calculate the square root of the right side: 0.484322105 Break this problem into two subproblems by setting (n + -0.1111111111) equal to 0.484322105 and -0.484322105.Subproblem 1
n + -0.1111111111 = 0.484322105 Simplifying n + -0.1111111111 = 0.484322105 Reorder the terms: -0.1111111111 + n = 0.484322105 Solving -0.1111111111 + n = 0.484322105 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1111111111 + n = 0.484322105 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + n = 0.484322105 + 0.1111111111 n = 0.484322105 + 0.1111111111 Combine like terms: 0.484322105 + 0.1111111111 = 0.5954332161 n = 0.5954332161 Simplifying n = 0.5954332161Subproblem 2
n + -0.1111111111 = -0.484322105 Simplifying n + -0.1111111111 = -0.484322105 Reorder the terms: -0.1111111111 + n = -0.484322105 Solving -0.1111111111 + n = -0.484322105 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1111111111 + n = -0.484322105 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + n = -0.484322105 + 0.1111111111 n = -0.484322105 + 0.1111111111 Combine like terms: -0.484322105 + 0.1111111111 = -0.3732109939 n = -0.3732109939 Simplifying n = -0.3732109939Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.5954332161, -0.3732109939}
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