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Simplifying 7n2 + -9n + -1 = 0 Reorder the terms: -1 + -9n + 7n2 = 0 Solving -1 + -9n + 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'. -0.1428571429 + -1.285714286n + n2 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + -1.285714286n + 0.1428571429 + n2 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + -1.285714286n + n2 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + -1.285714286n + n2 = 0 + 0.1428571429 -1.285714286n + n2 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 -1.285714286n + n2 = 0.1428571429 The n term is -1.285714286n. Take half its coefficient (-0.642857143). Square it (0.4132653063) and add it to both sides. Add '0.4132653063' to each side of the equation. -1.285714286n + 0.4132653063 + n2 = 0.1428571429 + 0.4132653063 Reorder the terms: 0.4132653063 + -1.285714286n + n2 = 0.1428571429 + 0.4132653063 Combine like terms: 0.1428571429 + 0.4132653063 = 0.5561224492 0.4132653063 + -1.285714286n + n2 = 0.5561224492 Factor a perfect square on the left side: (n + -0.642857143)(n + -0.642857143) = 0.5561224492 Calculate the square root of the right side: 0.745736179 Break this problem into two subproblems by setting (n + -0.642857143) equal to 0.745736179 and -0.745736179.Subproblem 1
n + -0.642857143 = 0.745736179 Simplifying n + -0.642857143 = 0.745736179 Reorder the terms: -0.642857143 + n = 0.745736179 Solving -0.642857143 + n = 0.745736179 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.642857143' to each side of the equation. -0.642857143 + 0.642857143 + n = 0.745736179 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + n = 0.745736179 + 0.642857143 n = 0.745736179 + 0.642857143 Combine like terms: 0.745736179 + 0.642857143 = 1.388593322 n = 1.388593322 Simplifying n = 1.388593322Subproblem 2
n + -0.642857143 = -0.745736179 Simplifying n + -0.642857143 = -0.745736179 Reorder the terms: -0.642857143 + n = -0.745736179 Solving -0.642857143 + n = -0.745736179 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.642857143' to each side of the equation. -0.642857143 + 0.642857143 + n = -0.745736179 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + n = -0.745736179 + 0.642857143 n = -0.745736179 + 0.642857143 Combine like terms: -0.745736179 + 0.642857143 = -0.102879036 n = -0.102879036 Simplifying n = -0.102879036Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.388593322, -0.102879036}
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