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Simplifying n2 + -18n + 18 = -10 Reorder the terms: 18 + -18n + n2 = -10 Solving 18 + -18n + n2 = -10 Solving for variable 'n'. Reorder the terms: 18 + 10 + -18n + n2 = -10 + 10 Combine like terms: 18 + 10 = 28 28 + -18n + n2 = -10 + 10 Combine like terms: -10 + 10 = 0 28 + -18n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-28' to each side of the equation. 28 + -18n + -28 + n2 = 0 + -28 Reorder the terms: 28 + -28 + -18n + n2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + -18n + n2 = 0 + -28 -18n + n2 = 0 + -28 Combine like terms: 0 + -28 = -28 -18n + n2 = -28 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 = -28 + 81 Reorder the terms: 81 + -18n + n2 = -28 + 81 Combine like terms: -28 + 81 = 53 81 + -18n + n2 = 53 Factor a perfect square on the left side: (n + -9)(n + -9) = 53 Calculate the square root of the right side: 7.280109889 Break this problem into two subproblems by setting (n + -9) equal to 7.280109889 and -7.280109889.Subproblem 1
n + -9 = 7.280109889 Simplifying n + -9 = 7.280109889 Reorder the terms: -9 + n = 7.280109889 Solving -9 + n = 7.280109889 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 = 7.280109889 + 9 Combine like terms: -9 + 9 = 0 0 + n = 7.280109889 + 9 n = 7.280109889 + 9 Combine like terms: 7.280109889 + 9 = 16.280109889 n = 16.280109889 Simplifying n = 16.280109889Subproblem 2
n + -9 = -7.280109889 Simplifying n + -9 = -7.280109889 Reorder the terms: -9 + n = -7.280109889 Solving -9 + n = -7.280109889 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 = -7.280109889 + 9 Combine like terms: -9 + 9 = 0 0 + n = -7.280109889 + 9 n = -7.280109889 + 9 Combine like terms: -7.280109889 + 9 = 1.719890111 n = 1.719890111 Simplifying n = 1.719890111Solution
The solution to the problem is based on the solutions from the subproblems. n = {16.280109889, 1.719890111}
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