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Simplifying n2 + -18n + -80 = 2 Reorder the terms: -80 + -18n + n2 = 2 Solving -80 + -18n + n2 = 2 Solving for variable 'n'. Reorder the terms: -80 + -2 + -18n + n2 = 2 + -2 Combine like terms: -80 + -2 = -82 -82 + -18n + n2 = 2 + -2 Combine like terms: 2 + -2 = 0 -82 + -18n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '82' to each side of the equation. -82 + -18n + 82 + n2 = 0 + 82 Reorder the terms: -82 + 82 + -18n + n2 = 0 + 82 Combine like terms: -82 + 82 = 0 0 + -18n + n2 = 0 + 82 -18n + n2 = 0 + 82 Combine like terms: 0 + 82 = 82 -18n + n2 = 82 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 = 82 + 81 Reorder the terms: 81 + -18n + n2 = 82 + 81 Combine like terms: 82 + 81 = 163 81 + -18n + n2 = 163 Factor a perfect square on the left side: (n + -9)(n + -9) = 163 Calculate the square root of the right side: 12.767145335 Break this problem into two subproblems by setting (n + -9) equal to 12.767145335 and -12.767145335.Subproblem 1
n + -9 = 12.767145335 Simplifying n + -9 = 12.767145335 Reorder the terms: -9 + n = 12.767145335 Solving -9 + n = 12.767145335 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 = 12.767145335 + 9 Combine like terms: -9 + 9 = 0 0 + n = 12.767145335 + 9 n = 12.767145335 + 9 Combine like terms: 12.767145335 + 9 = 21.767145335 n = 21.767145335 Simplifying n = 21.767145335Subproblem 2
n + -9 = -12.767145335 Simplifying n + -9 = -12.767145335 Reorder the terms: -9 + n = -12.767145335 Solving -9 + n = -12.767145335 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 = -12.767145335 + 9 Combine like terms: -9 + 9 = 0 0 + n = -12.767145335 + 9 n = -12.767145335 + 9 Combine like terms: -12.767145335 + 9 = -3.767145335 n = -3.767145335 Simplifying n = -3.767145335Solution
The solution to the problem is based on the solutions from the subproblems. n = {21.767145335, -3.767145335}
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