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Simplifying n2 + 18n + -4 = 0 Reorder the terms: -4 + 18n + n2 = 0 Solving -4 + 18n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 18n + 4 + n2 = 0 + 4 Reorder the terms: -4 + 4 + 18n + n2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 18n + n2 = 0 + 4 18n + n2 = 0 + 4 Combine like terms: 0 + 4 = 4 18n + n2 = 4 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 = 4 + 81 Reorder the terms: 81 + 18n + n2 = 4 + 81 Combine like terms: 4 + 81 = 85 81 + 18n + n2 = 85 Factor a perfect square on the left side: (n + 9)(n + 9) = 85 Calculate the square root of the right side: 9.219544457 Break this problem into two subproblems by setting (n + 9) equal to 9.219544457 and -9.219544457.Subproblem 1
n + 9 = 9.219544457 Simplifying n + 9 = 9.219544457 Reorder the terms: 9 + n = 9.219544457 Solving 9 + n = 9.219544457 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 = 9.219544457 + -9 Combine like terms: 9 + -9 = 0 0 + n = 9.219544457 + -9 n = 9.219544457 + -9 Combine like terms: 9.219544457 + -9 = 0.219544457 n = 0.219544457 Simplifying n = 0.219544457Subproblem 2
n + 9 = -9.219544457 Simplifying n + 9 = -9.219544457 Reorder the terms: 9 + n = -9.219544457 Solving 9 + n = -9.219544457 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 = -9.219544457 + -9 Combine like terms: 9 + -9 = 0 0 + n = -9.219544457 + -9 n = -9.219544457 + -9 Combine like terms: -9.219544457 + -9 = -18.219544457 n = -18.219544457 Simplifying n = -18.219544457Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.219544457, -18.219544457}
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