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Simplifying n2 + 6n + -46 = 0 Reorder the terms: -46 + 6n + n2 = 0 Solving -46 + 6n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '46' to each side of the equation. -46 + 6n + 46 + n2 = 0 + 46 Reorder the terms: -46 + 46 + 6n + n2 = 0 + 46 Combine like terms: -46 + 46 = 0 0 + 6n + n2 = 0 + 46 6n + n2 = 0 + 46 Combine like terms: 0 + 46 = 46 6n + n2 = 46 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 = 46 + 9 Reorder the terms: 9 + 6n + n2 = 46 + 9 Combine like terms: 46 + 9 = 55 9 + 6n + n2 = 55 Factor a perfect square on the left side: (n + 3)(n + 3) = 55 Calculate the square root of the right side: 7.416198487 Break this problem into two subproblems by setting (n + 3) equal to 7.416198487 and -7.416198487.Subproblem 1
n + 3 = 7.416198487 Simplifying n + 3 = 7.416198487 Reorder the terms: 3 + n = 7.416198487 Solving 3 + n = 7.416198487 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 = 7.416198487 + -3 Combine like terms: 3 + -3 = 0 0 + n = 7.416198487 + -3 n = 7.416198487 + -3 Combine like terms: 7.416198487 + -3 = 4.416198487 n = 4.416198487 Simplifying n = 4.416198487Subproblem 2
n + 3 = -7.416198487 Simplifying n + 3 = -7.416198487 Reorder the terms: 3 + n = -7.416198487 Solving 3 + n = -7.416198487 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 = -7.416198487 + -3 Combine like terms: 3 + -3 = 0 0 + n = -7.416198487 + -3 n = -7.416198487 + -3 Combine like terms: -7.416198487 + -3 = -10.416198487 n = -10.416198487 Simplifying n = -10.416198487Solution
The solution to the problem is based on the solutions from the subproblems. n = {4.416198487, -10.416198487}
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