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Simplifying n2 + 6n + -55 = 4 Reorder the terms: -55 + 6n + n2 = 4 Solving -55 + 6n + n2 = 4 Solving for variable 'n'. Reorder the terms: -55 + -4 + 6n + n2 = 4 + -4 Combine like terms: -55 + -4 = -59 -59 + 6n + n2 = 4 + -4 Combine like terms: 4 + -4 = 0 -59 + 6n + n2 = 0 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 = 5.246211251 n = 5.246211251 Simplifying n = 5.246211251Subproblem 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 = -11.246211251 n = -11.246211251 Simplifying n = -11.246211251Solution
The solution to the problem is based on the solutions from the subproblems. n = {5.246211251, -11.246211251}
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