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Simplifying n2 + -6n + -59 = 0 Reorder the terms: -59 + -6n + n2 = 0 Solving -59 + -6n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '59' to each side of the equation. -59 + -6n + 59 + n2 = 0 + 59 Reorder the terms: -59 + 59 + -6n + n2 = 0 + 59 Combine like terms: -59 + 59 = 0 0 + -6n + n2 = 0 + 59 -6n + n2 = 0 + 59 Combine like terms: 0 + 59 = 59 -6n + n2 = 59 The n term is -6n. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6n + 9 + n2 = 59 + 9 Reorder the terms: 9 + -6n + n2 = 59 + 9 Combine like terms: 59 + 9 = 68 9 + -6n + n2 = 68 Factor a perfect square on the left side: (n + -3)(n + -3) = 68 Calculate the square root of the right side: 8.246211251 Break this problem into two subproblems by setting (n + -3) equal to 8.246211251 and -8.246211251.Subproblem 1
n + -3 = 8.246211251 Simplifying n + -3 = 8.246211251 Reorder the terms: -3 + n = 8.246211251 Solving -3 + n = 8.246211251 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + n = 8.246211251 + 3 Combine like terms: -3 + 3 = 0 0 + n = 8.246211251 + 3 n = 8.246211251 + 3 Combine like terms: 8.246211251 + 3 = 11.246211251 n = 11.246211251 Simplifying n = 11.246211251Subproblem 2
n + -3 = -8.246211251 Simplifying n + -3 = -8.246211251 Reorder the terms: -3 + n = -8.246211251 Solving -3 + n = -8.246211251 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + n = -8.246211251 + 3 Combine like terms: -3 + 3 = 0 0 + n = -8.246211251 + 3 n = -8.246211251 + 3 Combine like terms: -8.246211251 + 3 = -5.246211251 n = -5.246211251 Simplifying n = -5.246211251Solution
The solution to the problem is based on the solutions from the subproblems. n = {11.246211251, -5.246211251}
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