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Simplifying N2 + -14N + -97 = 0 Reorder the terms: -97 + -14N + N2 = 0 Solving -97 + -14N + N2 = 0 Solving for variable 'N'. Begin completing the square. Move the constant term to the right: Add '97' to each side of the equation. -97 + -14N + 97 + N2 = 0 + 97 Reorder the terms: -97 + 97 + -14N + N2 = 0 + 97 Combine like terms: -97 + 97 = 0 0 + -14N + N2 = 0 + 97 -14N + N2 = 0 + 97 Combine like terms: 0 + 97 = 97 -14N + N2 = 97 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 = 97 + 49 Reorder the terms: 49 + -14N + N2 = 97 + 49 Combine like terms: 97 + 49 = 146 49 + -14N + N2 = 146 Factor a perfect square on the left side: (N + -7)(N + -7) = 146 Calculate the square root of the right side: 12.083045974 Break this problem into two subproblems by setting (N + -7) equal to 12.083045974 and -12.083045974.Subproblem 1
N + -7 = 12.083045974 Simplifying N + -7 = 12.083045974 Reorder the terms: -7 + N = 12.083045974 Solving -7 + N = 12.083045974 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 = 12.083045974 + 7 Combine like terms: -7 + 7 = 0 0 + N = 12.083045974 + 7 N = 12.083045974 + 7 Combine like terms: 12.083045974 + 7 = 19.083045974 N = 19.083045974 Simplifying N = 19.083045974Subproblem 2
N + -7 = -12.083045974 Simplifying N + -7 = -12.083045974 Reorder the terms: -7 + N = -12.083045974 Solving -7 + N = -12.083045974 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 = -12.083045974 + 7 Combine like terms: -7 + 7 = 0 0 + N = -12.083045974 + 7 N = -12.083045974 + 7 Combine like terms: -12.083045974 + 7 = -5.083045974 N = -5.083045974 Simplifying N = -5.083045974Solution
The solution to the problem is based on the solutions from the subproblems. N = {19.083045974, -5.083045974}
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