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Simplifying n2 + 18n + 42 = 5 Reorder the terms: 42 + 18n + n2 = 5 Solving 42 + 18n + n2 = 5 Solving for variable 'n'. Reorder the terms: 42 + -5 + 18n + n2 = 5 + -5 Combine like terms: 42 + -5 = 37 37 + 18n + n2 = 5 + -5 Combine like terms: 5 + -5 = 0 37 + 18n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-37' to each side of the equation. 37 + 18n + -37 + n2 = 0 + -37 Reorder the terms: 37 + -37 + 18n + n2 = 0 + -37 Combine like terms: 37 + -37 = 0 0 + 18n + n2 = 0 + -37 18n + n2 = 0 + -37 Combine like terms: 0 + -37 = -37 18n + n2 = -37 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 = -37 + 81 Reorder the terms: 81 + 18n + n2 = -37 + 81 Combine like terms: -37 + 81 = 44 81 + 18n + n2 = 44 Factor a perfect square on the left side: (n + 9)(n + 9) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (n + 9) equal to 6.633249581 and -6.633249581.Subproblem 1
n + 9 = 6.633249581 Simplifying n + 9 = 6.633249581 Reorder the terms: 9 + n = 6.633249581 Solving 9 + n = 6.633249581 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 = 6.633249581 + -9 Combine like terms: 9 + -9 = 0 0 + n = 6.633249581 + -9 n = 6.633249581 + -9 Combine like terms: 6.633249581 + -9 = -2.366750419 n = -2.366750419 Simplifying n = -2.366750419Subproblem 2
n + 9 = -6.633249581 Simplifying n + 9 = -6.633249581 Reorder the terms: 9 + n = -6.633249581 Solving 9 + n = -6.633249581 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 = -6.633249581 + -9 Combine like terms: 9 + -9 = 0 0 + n = -6.633249581 + -9 n = -6.633249581 + -9 Combine like terms: -6.633249581 + -9 = -15.633249581 n = -15.633249581 Simplifying n = -15.633249581Solution
The solution to the problem is based on the solutions from the subproblems. n = {-2.366750419, -15.633249581}
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