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Simplifying n2 + 12n + -59 = -4 Reorder the terms: -59 + 12n + n2 = -4 Solving -59 + 12n + n2 = -4 Solving for variable 'n'. Reorder the terms: -59 + 4 + 12n + n2 = -4 + 4 Combine like terms: -59 + 4 = -55 -55 + 12n + n2 = -4 + 4 Combine like terms: -4 + 4 = 0 -55 + 12n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '55' to each side of the equation. -55 + 12n + 55 + n2 = 0 + 55 Reorder the terms: -55 + 55 + 12n + n2 = 0 + 55 Combine like terms: -55 + 55 = 0 0 + 12n + n2 = 0 + 55 12n + n2 = 0 + 55 Combine like terms: 0 + 55 = 55 12n + n2 = 55 The n term is 12n. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12n + 36 + n2 = 55 + 36 Reorder the terms: 36 + 12n + n2 = 55 + 36 Combine like terms: 55 + 36 = 91 36 + 12n + n2 = 91 Factor a perfect square on the left side: (n + 6)(n + 6) = 91 Calculate the square root of the right side: 9.539392014 Break this problem into two subproblems by setting (n + 6) equal to 9.539392014 and -9.539392014.Subproblem 1
n + 6 = 9.539392014 Simplifying n + 6 = 9.539392014 Reorder the terms: 6 + n = 9.539392014 Solving 6 + n = 9.539392014 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + n = 9.539392014 + -6 Combine like terms: 6 + -6 = 0 0 + n = 9.539392014 + -6 n = 9.539392014 + -6 Combine like terms: 9.539392014 + -6 = 3.539392014 n = 3.539392014 Simplifying n = 3.539392014Subproblem 2
n + 6 = -9.539392014 Simplifying n + 6 = -9.539392014 Reorder the terms: 6 + n = -9.539392014 Solving 6 + n = -9.539392014 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + n = -9.539392014 + -6 Combine like terms: 6 + -6 = 0 0 + n = -9.539392014 + -6 n = -9.539392014 + -6 Combine like terms: -9.539392014 + -6 = -15.539392014 n = -15.539392014 Simplifying n = -15.539392014Solution
The solution to the problem is based on the solutions from the subproblems. n = {3.539392014, -15.539392014}
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