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Simplifying N2 + -14N + 49 = 3 Reorder the terms: 49 + -14N + N2 = 3 Solving 49 + -14N + N2 = 3 Solving for variable 'N'. Reorder the terms: 49 + -3 + -14N + N2 = 3 + -3 Combine like terms: 49 + -3 = 46 46 + -14N + N2 = 3 + -3 Combine like terms: 3 + -3 = 0 46 + -14N + N2 = 0 Begin completing the square. Move the constant term to the right: Add '-46' to each side of the equation. 46 + -14N + -46 + N2 = 0 + -46 Reorder the terms: 46 + -46 + -14N + N2 = 0 + -46 Combine like terms: 46 + -46 = 0 0 + -14N + N2 = 0 + -46 -14N + N2 = 0 + -46 Combine like terms: 0 + -46 = -46 -14N + N2 = -46 The N term is -14N. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14N + 49 + N2 = -46 + 49 Reorder the terms: 49 + -14N + N2 = -46 + 49 Combine like terms: -46 + 49 = 3 49 + -14N + N2 = 3 Factor a perfect square on the left side: (N + -7)(N + -7) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (N + -7) equal to 1.732050808 and -1.732050808.Subproblem 1
N + -7 = 1.732050808 Simplifying N + -7 = 1.732050808 Reorder the terms: -7 + N = 1.732050808 Solving -7 + N = 1.732050808 Solving for variable 'N'. Move all terms containing N to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + N = 1.732050808 + 7 Combine like terms: -7 + 7 = 0 0 + N = 1.732050808 + 7 N = 1.732050808 + 7 Combine like terms: 1.732050808 + 7 = 8.732050808 N = 8.732050808 Simplifying N = 8.732050808Subproblem 2
N + -7 = -1.732050808 Simplifying N + -7 = -1.732050808 Reorder the terms: -7 + N = -1.732050808 Solving -7 + N = -1.732050808 Solving for variable 'N'. Move all terms containing N to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + N = -1.732050808 + 7 Combine like terms: -7 + 7 = 0 0 + N = -1.732050808 + 7 N = -1.732050808 + 7 Combine like terms: -1.732050808 + 7 = 5.267949192 N = 5.267949192 Simplifying N = 5.267949192Solution
The solution to the problem is based on the solutions from the subproblems. N = {8.732050808, 5.267949192}
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