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Simplifying n2 + 18n + 50 = 0 Reorder the terms: 50 + 18n + n2 = 0 Solving 50 + 18n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '-50' to each side of the equation. 50 + 18n + -50 + n2 = 0 + -50 Reorder the terms: 50 + -50 + 18n + n2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + 18n + n2 = 0 + -50 18n + n2 = 0 + -50 Combine like terms: 0 + -50 = -50 18n + n2 = -50 The n term is 18n. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18n + 81 + n2 = -50 + 81 Reorder the terms: 81 + 18n + n2 = -50 + 81 Combine like terms: -50 + 81 = 31 81 + 18n + n2 = 31 Factor a perfect square on the left side: (n + 9)(n + 9) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (n + 9) equal to 5.567764363 and -5.567764363.Subproblem 1
n + 9 = 5.567764363 Simplifying n + 9 = 5.567764363 Reorder the terms: 9 + n = 5.567764363 Solving 9 + n = 5.567764363 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + n = 5.567764363 + -9 Combine like terms: 9 + -9 = 0 0 + n = 5.567764363 + -9 n = 5.567764363 + -9 Combine like terms: 5.567764363 + -9 = -3.432235637 n = -3.432235637 Simplifying n = -3.432235637Subproblem 2
n + 9 = -5.567764363 Simplifying n + 9 = -5.567764363 Reorder the terms: 9 + n = -5.567764363 Solving 9 + n = -5.567764363 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + n = -5.567764363 + -9 Combine like terms: 9 + -9 = 0 0 + n = -5.567764363 + -9 n = -5.567764363 + -9 Combine like terms: -5.567764363 + -9 = -14.567764363 n = -14.567764363 Simplifying n = -14.567764363Solution
The solution to the problem is based on the solutions from the subproblems. n = {-3.432235637, -14.567764363}
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