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Simplifying N2 + -10N + -25 = 0 Reorder the terms: -25 + -10N + N2 = 0 Solving -25 + -10N + N2 = 0 Solving for variable 'N'. Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + -10N + 25 + N2 = 0 + 25 Reorder the terms: -25 + 25 + -10N + N2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -10N + N2 = 0 + 25 -10N + N2 = 0 + 25 Combine like terms: 0 + 25 = 25 -10N + N2 = 25 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 = 25 + 25 Reorder the terms: 25 + -10N + N2 = 25 + 25 Combine like terms: 25 + 25 = 50 25 + -10N + N2 = 50 Factor a perfect square on the left side: (N + -5)(N + -5) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (N + -5) equal to 7.071067812 and -7.071067812.Subproblem 1
N + -5 = 7.071067812 Simplifying N + -5 = 7.071067812 Reorder the terms: -5 + N = 7.071067812 Solving -5 + N = 7.071067812 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 = 7.071067812 + 5 Combine like terms: -5 + 5 = 0 0 + N = 7.071067812 + 5 N = 7.071067812 + 5 Combine like terms: 7.071067812 + 5 = 12.071067812 N = 12.071067812 Simplifying N = 12.071067812Subproblem 2
N + -5 = -7.071067812 Simplifying N + -5 = -7.071067812 Reorder the terms: -5 + N = -7.071067812 Solving -5 + N = -7.071067812 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 = -7.071067812 + 5 Combine like terms: -5 + 5 = 0 0 + N = -7.071067812 + 5 N = -7.071067812 + 5 Combine like terms: -7.071067812 + 5 = -2.071067812 N = -2.071067812 Simplifying N = -2.071067812Solution
The solution to the problem is based on the solutions from the subproblems. N = {12.071067812, -2.071067812}
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