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Simplifying 9n2 + -2n + -41 = 0 Reorder the terms: -41 + -2n + 9n2 = 0 Solving -41 + -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'. -4.555555556 + -0.2222222222n + n2 = 0 Move the constant term to the right: Add '4.555555556' to each side of the equation. -4.555555556 + -0.2222222222n + 4.555555556 + n2 = 0 + 4.555555556 Reorder the terms: -4.555555556 + 4.555555556 + -0.2222222222n + n2 = 0 + 4.555555556 Combine like terms: -4.555555556 + 4.555555556 = 0.000000000 0.000000000 + -0.2222222222n + n2 = 0 + 4.555555556 -0.2222222222n + n2 = 0 + 4.555555556 Combine like terms: 0 + 4.555555556 = 4.555555556 -0.2222222222n + n2 = 4.555555556 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 = 4.555555556 + 0.01234567901 Reorder the terms: 0.01234567901 + -0.2222222222n + n2 = 4.555555556 + 0.01234567901 Combine like terms: 4.555555556 + 0.01234567901 = 4.56790123501 0.01234567901 + -0.2222222222n + n2 = 4.56790123501 Factor a perfect square on the left side: (n + -0.1111111111)(n + -0.1111111111) = 4.56790123501 Calculate the square root of the right side: 2.137264896 Break this problem into two subproblems by setting (n + -0.1111111111) equal to 2.137264896 and -2.137264896.Subproblem 1
n + -0.1111111111 = 2.137264896 Simplifying n + -0.1111111111 = 2.137264896 Reorder the terms: -0.1111111111 + n = 2.137264896 Solving -0.1111111111 + n = 2.137264896 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 = 2.137264896 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + n = 2.137264896 + 0.1111111111 n = 2.137264896 + 0.1111111111 Combine like terms: 2.137264896 + 0.1111111111 = 2.2483760071 n = 2.2483760071 Simplifying n = 2.2483760071Subproblem 2
n + -0.1111111111 = -2.137264896 Simplifying n + -0.1111111111 = -2.137264896 Reorder the terms: -0.1111111111 + n = -2.137264896 Solving -0.1111111111 + n = -2.137264896 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 = -2.137264896 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + n = -2.137264896 + 0.1111111111 n = -2.137264896 + 0.1111111111 Combine like terms: -2.137264896 + 0.1111111111 = -2.0261537849 n = -2.0261537849 Simplifying n = -2.0261537849Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.2483760071, -2.0261537849}
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