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Simplifying 7n2 + -58n + -35 = 0 Reorder the terms: -35 + -58n + 7n2 = 0 Solving -35 + -58n + 7n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -5 + -8.285714286n + n2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -8.285714286n + 5 + n2 = 0 + 5 Reorder the terms: -5 + 5 + -8.285714286n + n2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -8.285714286n + n2 = 0 + 5 -8.285714286n + n2 = 0 + 5 Combine like terms: 0 + 5 = 5 -8.285714286n + n2 = 5 The n term is -8.285714286n. Take half its coefficient (-4.142857143). Square it (17.16326531) and add it to both sides. Add '17.16326531' to each side of the equation. -8.285714286n + 17.16326531 + n2 = 5 + 17.16326531 Reorder the terms: 17.16326531 + -8.285714286n + n2 = 5 + 17.16326531 Combine like terms: 5 + 17.16326531 = 22.16326531 17.16326531 + -8.285714286n + n2 = 22.16326531 Factor a perfect square on the left side: (n + -4.142857143)(n + -4.142857143) = 22.16326531 Calculate the square root of the right side: 4.70778773 Break this problem into two subproblems by setting (n + -4.142857143) equal to 4.70778773 and -4.70778773.Subproblem 1
n + -4.142857143 = 4.70778773 Simplifying n + -4.142857143 = 4.70778773 Reorder the terms: -4.142857143 + n = 4.70778773 Solving -4.142857143 + n = 4.70778773 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4.142857143' to each side of the equation. -4.142857143 + 4.142857143 + n = 4.70778773 + 4.142857143 Combine like terms: -4.142857143 + 4.142857143 = 0.000000000 0.000000000 + n = 4.70778773 + 4.142857143 n = 4.70778773 + 4.142857143 Combine like terms: 4.70778773 + 4.142857143 = 8.850644873 n = 8.850644873 Simplifying n = 8.850644873Subproblem 2
n + -4.142857143 = -4.70778773 Simplifying n + -4.142857143 = -4.70778773 Reorder the terms: -4.142857143 + n = -4.70778773 Solving -4.142857143 + n = -4.70778773 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4.142857143' to each side of the equation. -4.142857143 + 4.142857143 + n = -4.70778773 + 4.142857143 Combine like terms: -4.142857143 + 4.142857143 = 0.000000000 0.000000000 + n = -4.70778773 + 4.142857143 n = -4.70778773 + 4.142857143 Combine like terms: -4.70778773 + 4.142857143 = -0.564930587 n = -0.564930587 Simplifying n = -0.564930587Solution
The solution to the problem is based on the solutions from the subproblems. n = {8.850644873, -0.564930587}
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