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Simplifying N2 + -10N + -73 = -9 Reorder the terms: -73 + -10N + N2 = -9 Solving -73 + -10N + N2 = -9 Solving for variable 'N'. Reorder the terms: -73 + 9 + -10N + N2 = -9 + 9 Combine like terms: -73 + 9 = -64 -64 + -10N + N2 = -9 + 9 Combine like terms: -9 + 9 = 0 -64 + -10N + N2 = 0 Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + -10N + 64 + N2 = 0 + 64 Reorder the terms: -64 + 64 + -10N + N2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + -10N + N2 = 0 + 64 -10N + N2 = 0 + 64 Combine like terms: 0 + 64 = 64 -10N + N2 = 64 The N term is -10N. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10N + 25 + N2 = 64 + 25 Reorder the terms: 25 + -10N + N2 = 64 + 25 Combine like terms: 64 + 25 = 89 25 + -10N + N2 = 89 Factor a perfect square on the left side: (N + -5)(N + -5) = 89 Calculate the square root of the right side: 9.433981132 Break this problem into two subproblems by setting (N + -5) equal to 9.433981132 and -9.433981132.Subproblem 1
N + -5 = 9.433981132 Simplifying N + -5 = 9.433981132 Reorder the terms: -5 + N = 9.433981132 Solving -5 + N = 9.433981132 Solving for variable 'N'. Move all terms containing N to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + N = 9.433981132 + 5 Combine like terms: -5 + 5 = 0 0 + N = 9.433981132 + 5 N = 9.433981132 + 5 Combine like terms: 9.433981132 + 5 = 14.433981132 N = 14.433981132 Simplifying N = 14.433981132Subproblem 2
N + -5 = -9.433981132 Simplifying N + -5 = -9.433981132 Reorder the terms: -5 + N = -9.433981132 Solving -5 + N = -9.433981132 Solving for variable 'N'. Move all terms containing N to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + N = -9.433981132 + 5 Combine like terms: -5 + 5 = 0 0 + N = -9.433981132 + 5 N = -9.433981132 + 5 Combine like terms: -9.433981132 + 5 = -4.433981132 N = -4.433981132 Simplifying N = -4.433981132Solution
The solution to the problem is based on the solutions from the subproblems. N = {14.433981132, -4.433981132}
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