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Simplifying n2 + 6n + -4 = 0 Reorder the terms: -4 + 6n + n2 = 0 Solving -4 + 6n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 6n + 4 + n2 = 0 + 4 Reorder the terms: -4 + 4 + 6n + n2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 6n + n2 = 0 + 4 6n + n2 = 0 + 4 Combine like terms: 0 + 4 = 4 6n + n2 = 4 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 = 4 + 9 Reorder the terms: 9 + 6n + n2 = 4 + 9 Combine like terms: 4 + 9 = 13 9 + 6n + n2 = 13 Factor a perfect square on the left side: (n + 3)(n + 3) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (n + 3) equal to 3.605551275 and -3.605551275.Subproblem 1
n + 3 = 3.605551275 Simplifying n + 3 = 3.605551275 Reorder the terms: 3 + n = 3.605551275 Solving 3 + n = 3.605551275 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 = 3.605551275 + -3 Combine like terms: 3 + -3 = 0 0 + n = 3.605551275 + -3 n = 3.605551275 + -3 Combine like terms: 3.605551275 + -3 = 0.605551275 n = 0.605551275 Simplifying n = 0.605551275Subproblem 2
n + 3 = -3.605551275 Simplifying n + 3 = -3.605551275 Reorder the terms: 3 + n = -3.605551275 Solving 3 + n = -3.605551275 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 = -3.605551275 + -3 Combine like terms: 3 + -3 = 0 0 + n = -3.605551275 + -3 n = -3.605551275 + -3 Combine like terms: -3.605551275 + -3 = -6.605551275 n = -6.605551275 Simplifying n = -6.605551275Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.605551275, -6.605551275}
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