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Simplifying 14n2 + 17n + -18 = 0 Reorder the terms: -18 + 17n + 14n2 = 0 Solving -18 + 17n + 14n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -1.285714286 + 1.214285714n + n2 = 0 Move the constant term to the right: Add '1.285714286' to each side of the equation. -1.285714286 + 1.214285714n + 1.285714286 + n2 = 0 + 1.285714286 Reorder the terms: -1.285714286 + 1.285714286 + 1.214285714n + n2 = 0 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + 1.214285714n + n2 = 0 + 1.285714286 1.214285714n + n2 = 0 + 1.285714286 Combine like terms: 0 + 1.285714286 = 1.285714286 1.214285714n + n2 = 1.285714286 The n term is 1.214285714n. Take half its coefficient (0.607142857). Square it (0.3686224488) and add it to both sides. Add '0.3686224488' to each side of the equation. 1.214285714n + 0.3686224488 + n2 = 1.285714286 + 0.3686224488 Reorder the terms: 0.3686224488 + 1.214285714n + n2 = 1.285714286 + 0.3686224488 Combine like terms: 1.285714286 + 0.3686224488 = 1.6543367348 0.3686224488 + 1.214285714n + n2 = 1.6543367348 Factor a perfect square on the left side: (n + 0.607142857)(n + 0.607142857) = 1.6543367348 Calculate the square root of the right side: 1.286210222 Break this problem into two subproblems by setting (n + 0.607142857) equal to 1.286210222 and -1.286210222.Subproblem 1
n + 0.607142857 = 1.286210222 Simplifying n + 0.607142857 = 1.286210222 Reorder the terms: 0.607142857 + n = 1.286210222 Solving 0.607142857 + n = 1.286210222 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.607142857' to each side of the equation. 0.607142857 + -0.607142857 + n = 1.286210222 + -0.607142857 Combine like terms: 0.607142857 + -0.607142857 = 0.000000000 0.000000000 + n = 1.286210222 + -0.607142857 n = 1.286210222 + -0.607142857 Combine like terms: 1.286210222 + -0.607142857 = 0.679067365 n = 0.679067365 Simplifying n = 0.679067365Subproblem 2
n + 0.607142857 = -1.286210222 Simplifying n + 0.607142857 = -1.286210222 Reorder the terms: 0.607142857 + n = -1.286210222 Solving 0.607142857 + n = -1.286210222 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.607142857' to each side of the equation. 0.607142857 + -0.607142857 + n = -1.286210222 + -0.607142857 Combine like terms: 0.607142857 + -0.607142857 = 0.000000000 0.000000000 + n = -1.286210222 + -0.607142857 n = -1.286210222 + -0.607142857 Combine like terms: -1.286210222 + -0.607142857 = -1.893353079 n = -1.893353079 Simplifying n = -1.893353079Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.679067365, -1.893353079}
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