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Simplifying 28n2 = -96 + -183n Solving 28n2 = -96 + -183n Solving for variable 'n'. Reorder the terms: 96 + 183n + 28n2 = -96 + -183n + 96 + 183n Reorder the terms: 96 + 183n + 28n2 = -96 + 96 + -183n + 183n Combine like terms: -96 + 96 = 0 96 + 183n + 28n2 = 0 + -183n + 183n 96 + 183n + 28n2 = -183n + 183n Combine like terms: -183n + 183n = 0 96 + 183n + 28n2 = 0 Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. 3.428571429 + 6.535714286n + n2 = 0 Move the constant term to the right: Add '-3.428571429' to each side of the equation. 3.428571429 + 6.535714286n + -3.428571429 + n2 = 0 + -3.428571429 Reorder the terms: 3.428571429 + -3.428571429 + 6.535714286n + n2 = 0 + -3.428571429 Combine like terms: 3.428571429 + -3.428571429 = 0.000000000 0.000000000 + 6.535714286n + n2 = 0 + -3.428571429 6.535714286n + n2 = 0 + -3.428571429 Combine like terms: 0 + -3.428571429 = -3.428571429 6.535714286n + n2 = -3.428571429 The n term is 6.535714286n. Take half its coefficient (3.267857143). Square it (10.67889031) and add it to both sides. Add '10.67889031' to each side of the equation. 6.535714286n + 10.67889031 + n2 = -3.428571429 + 10.67889031 Reorder the terms: 10.67889031 + 6.535714286n + n2 = -3.428571429 + 10.67889031 Combine like terms: -3.428571429 + 10.67889031 = 7.250318881 10.67889031 + 6.535714286n + n2 = 7.250318881 Factor a perfect square on the left side: (n + 3.267857143)(n + 3.267857143) = 7.250318881 Calculate the square root of the right side: 2.692641618 Break this problem into two subproblems by setting (n + 3.267857143) equal to 2.692641618 and -2.692641618.Subproblem 1
n + 3.267857143 = 2.692641618 Simplifying n + 3.267857143 = 2.692641618 Reorder the terms: 3.267857143 + n = 2.692641618 Solving 3.267857143 + n = 2.692641618 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3.267857143' to each side of the equation. 3.267857143 + -3.267857143 + n = 2.692641618 + -3.267857143 Combine like terms: 3.267857143 + -3.267857143 = 0.000000000 0.000000000 + n = 2.692641618 + -3.267857143 n = 2.692641618 + -3.267857143 Combine like terms: 2.692641618 + -3.267857143 = -0.575215525 n = -0.575215525 Simplifying n = -0.575215525Subproblem 2
n + 3.267857143 = -2.692641618 Simplifying n + 3.267857143 = -2.692641618 Reorder the terms: 3.267857143 + n = -2.692641618 Solving 3.267857143 + n = -2.692641618 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3.267857143' to each side of the equation. 3.267857143 + -3.267857143 + n = -2.692641618 + -3.267857143 Combine like terms: 3.267857143 + -3.267857143 = 0.000000000 0.000000000 + n = -2.692641618 + -3.267857143 n = -2.692641618 + -3.267857143 Combine like terms: -2.692641618 + -3.267857143 = -5.960498761 n = -5.960498761 Simplifying n = -5.960498761Solution
The solution to the problem is based on the solutions from the subproblems. n = {-0.575215525, -5.960498761}
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