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Simplifying n2 + -18n + -37 = -8 Reorder the terms: -37 + -18n + n2 = -8 Solving -37 + -18n + n2 = -8 Solving for variable 'n'. Reorder the terms: -37 + 8 + -18n + n2 = -8 + 8 Combine like terms: -37 + 8 = -29 -29 + -18n + n2 = -8 + 8 Combine like terms: -8 + 8 = 0 -29 + -18n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + -18n + 29 + n2 = 0 + 29 Reorder the terms: -29 + 29 + -18n + n2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + -18n + n2 = 0 + 29 -18n + n2 = 0 + 29 Combine like terms: 0 + 29 = 29 -18n + n2 = 29 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 = 29 + 81 Reorder the terms: 81 + -18n + n2 = 29 + 81 Combine like terms: 29 + 81 = 110 81 + -18n + n2 = 110 Factor a perfect square on the left side: (n + -9)(n + -9) = 110 Calculate the square root of the right side: 10.488088482 Break this problem into two subproblems by setting (n + -9) equal to 10.488088482 and -10.488088482.Subproblem 1
n + -9 = 10.488088482 Simplifying n + -9 = 10.488088482 Reorder the terms: -9 + n = 10.488088482 Solving -9 + n = 10.488088482 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 = 10.488088482 + 9 Combine like terms: -9 + 9 = 0 0 + n = 10.488088482 + 9 n = 10.488088482 + 9 Combine like terms: 10.488088482 + 9 = 19.488088482 n = 19.488088482 Simplifying n = 19.488088482Subproblem 2
n + -9 = -10.488088482 Simplifying n + -9 = -10.488088482 Reorder the terms: -9 + n = -10.488088482 Solving -9 + n = -10.488088482 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 = -10.488088482 + 9 Combine like terms: -9 + 9 = 0 0 + n = -10.488088482 + 9 n = -10.488088482 + 9 Combine like terms: -10.488088482 + 9 = -1.488088482 n = -1.488088482 Simplifying n = -1.488088482Solution
The solution to the problem is based on the solutions from the subproblems. n = {19.488088482, -1.488088482}
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