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Simplifying n2 + -18n + -36 = 0 Reorder the terms: -36 + -18n + n2 = 0 Solving -36 + -18n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -18n + 36 + n2 = 0 + 36 Reorder the terms: -36 + 36 + -18n + n2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -18n + n2 = 0 + 36 -18n + n2 = 0 + 36 Combine like terms: 0 + 36 = 36 -18n + n2 = 36 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 = 36 + 81 Reorder the terms: 81 + -18n + n2 = 36 + 81 Combine like terms: 36 + 81 = 117 81 + -18n + n2 = 117 Factor a perfect square on the left side: (n + -9)(n + -9) = 117 Calculate the square root of the right side: 10.816653826 Break this problem into two subproblems by setting (n + -9) equal to 10.816653826 and -10.816653826.Subproblem 1
n + -9 = 10.816653826 Simplifying n + -9 = 10.816653826 Reorder the terms: -9 + n = 10.816653826 Solving -9 + n = 10.816653826 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 = 10.816653826 + 9 Combine like terms: -9 + 9 = 0 0 + n = 10.816653826 + 9 n = 10.816653826 + 9 Combine like terms: 10.816653826 + 9 = 19.816653826 n = 19.816653826 Simplifying n = 19.816653826Subproblem 2
n + -9 = -10.816653826 Simplifying n + -9 = -10.816653826 Reorder the terms: -9 + n = -10.816653826 Solving -9 + n = -10.816653826 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 = -10.816653826 + 9 Combine like terms: -9 + 9 = 0 0 + n = -10.816653826 + 9 n = -10.816653826 + 9 Combine like terms: -10.816653826 + 9 = -1.816653826 n = -1.816653826 Simplifying n = -1.816653826Solution
The solution to the problem is based on the solutions from the subproblems. n = {19.816653826, -1.816653826}
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