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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 = 2.071067812 n = 2.071067812 Simplifying n = 2.071067812Subproblem 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 = -12.071067812 n = -12.071067812 Simplifying n = -12.071067812Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.071067812, -12.071067812}
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