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Simplifying 2n2 + -1n + -18 = 0 Reorder the terms: -18 + -1n + 2n2 = 0 Solving -18 + -1n + 2n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -9 + -0.5n + n2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -0.5n + 9 + n2 = 0 + 9 Reorder the terms: -9 + 9 + -0.5n + n2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -0.5n + n2 = 0 + 9 -0.5n + n2 = 0 + 9 Combine like terms: 0 + 9 = 9 -0.5n + n2 = 9 The n term is -0.5n. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5n + 0.0625 + n2 = 9 + 0.0625 Reorder the terms: 0.0625 + -0.5n + n2 = 9 + 0.0625 Combine like terms: 9 + 0.0625 = 9.0625 0.0625 + -0.5n + n2 = 9.0625 Factor a perfect square on the left side: (n + -0.25)(n + -0.25) = 9.0625 Calculate the square root of the right side: 3.010398645 Break this problem into two subproblems by setting (n + -0.25) equal to 3.010398645 and -3.010398645.Subproblem 1
n + -0.25 = 3.010398645 Simplifying n + -0.25 = 3.010398645 Reorder the terms: -0.25 + n = 3.010398645 Solving -0.25 + n = 3.010398645 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + n = 3.010398645 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + n = 3.010398645 + 0.25 n = 3.010398645 + 0.25 Combine like terms: 3.010398645 + 0.25 = 3.260398645 n = 3.260398645 Simplifying n = 3.260398645Subproblem 2
n + -0.25 = -3.010398645 Simplifying n + -0.25 = -3.010398645 Reorder the terms: -0.25 + n = -3.010398645 Solving -0.25 + n = -3.010398645 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + n = -3.010398645 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + n = -3.010398645 + 0.25 n = -3.010398645 + 0.25 Combine like terms: -3.010398645 + 0.25 = -2.760398645 n = -2.760398645 Simplifying n = -2.760398645Solution
The solution to the problem is based on the solutions from the subproblems. n = {3.260398645, -2.760398645}
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