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Simplifying n2 + 4n + -60 = 4 Reorder the terms: -60 + 4n + n2 = 4 Solving -60 + 4n + n2 = 4 Solving for variable 'n'. Reorder the terms: -60 + -4 + 4n + n2 = 4 + -4 Combine like terms: -60 + -4 = -64 -64 + 4n + n2 = 4 + -4 Combine like terms: 4 + -4 = 0 -64 + 4n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + 4n + 64 + n2 = 0 + 64 Reorder the terms: -64 + 64 + 4n + n2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 4n + n2 = 0 + 64 4n + n2 = 0 + 64 Combine like terms: 0 + 64 = 64 4n + n2 = 64 The n term is 4n. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4n + 4 + n2 = 64 + 4 Reorder the terms: 4 + 4n + n2 = 64 + 4 Combine like terms: 64 + 4 = 68 4 + 4n + n2 = 68 Factor a perfect square on the left side: (n + 2)(n + 2) = 68 Calculate the square root of the right side: 8.246211251 Break this problem into two subproblems by setting (n + 2) equal to 8.246211251 and -8.246211251.Subproblem 1
n + 2 = 8.246211251 Simplifying n + 2 = 8.246211251 Reorder the terms: 2 + n = 8.246211251 Solving 2 + n = 8.246211251 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + n = 8.246211251 + -2 Combine like terms: 2 + -2 = 0 0 + n = 8.246211251 + -2 n = 8.246211251 + -2 Combine like terms: 8.246211251 + -2 = 6.246211251 n = 6.246211251 Simplifying n = 6.246211251Subproblem 2
n + 2 = -8.246211251 Simplifying n + 2 = -8.246211251 Reorder the terms: 2 + n = -8.246211251 Solving 2 + n = -8.246211251 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + n = -8.246211251 + -2 Combine like terms: 2 + -2 = 0 0 + n = -8.246211251 + -2 n = -8.246211251 + -2 Combine like terms: -8.246211251 + -2 = -10.246211251 n = -10.246211251 Simplifying n = -10.246211251Solution
The solution to the problem is based on the solutions from the subproblems. n = {6.246211251, -10.246211251}
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