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Simplifying 2n2 + -17n + -6 = 0 Reorder the terms: -6 + -17n + 2n2 = 0 Solving -6 + -17n + 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'. -3 + -8.5n + n2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -8.5n + 3 + n2 = 0 + 3 Reorder the terms: -3 + 3 + -8.5n + n2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -8.5n + n2 = 0 + 3 -8.5n + n2 = 0 + 3 Combine like terms: 0 + 3 = 3 -8.5n + n2 = 3 The n term is -8.5n. Take half its coefficient (-4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. -8.5n + 18.0625 + n2 = 3 + 18.0625 Reorder the terms: 18.0625 + -8.5n + n2 = 3 + 18.0625 Combine like terms: 3 + 18.0625 = 21.0625 18.0625 + -8.5n + n2 = 21.0625 Factor a perfect square on the left side: (n + -4.25)(n + -4.25) = 21.0625 Calculate the square root of the right side: 4.589389938 Break this problem into two subproblems by setting (n + -4.25) equal to 4.589389938 and -4.589389938.Subproblem 1
n + -4.25 = 4.589389938 Simplifying n + -4.25 = 4.589389938 Reorder the terms: -4.25 + n = 4.589389938 Solving -4.25 + n = 4.589389938 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + n = 4.589389938 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + n = 4.589389938 + 4.25 n = 4.589389938 + 4.25 Combine like terms: 4.589389938 + 4.25 = 8.839389938 n = 8.839389938 Simplifying n = 8.839389938Subproblem 2
n + -4.25 = -4.589389938 Simplifying n + -4.25 = -4.589389938 Reorder the terms: -4.25 + n = -4.589389938 Solving -4.25 + n = -4.589389938 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + n = -4.589389938 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + n = -4.589389938 + 4.25 n = -4.589389938 + 4.25 Combine like terms: -4.589389938 + 4.25 = -0.339389938 n = -0.339389938 Simplifying n = -0.339389938Solution
The solution to the problem is based on the solutions from the subproblems. n = {8.839389938, -0.339389938}
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