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Simplifying 2n2 + -6n = 5 Reorder the terms: -6n + 2n2 = 5 Solving -6n + 2n2 = 5 Solving for variable 'n'. Reorder the terms: -5 + -6n + 2n2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + -6n + 2n2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + -3n + n2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -3n + 2.5 + n2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -3n + n2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -3n + n2 = 0 + 2.5 -3n + n2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -3n + n2 = 2.5 The n term is -3n. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3n + 2.25 + n2 = 2.5 + 2.25 Reorder the terms: 2.25 + -3n + n2 = 2.5 + 2.25 Combine like terms: 2.5 + 2.25 = 4.75 2.25 + -3n + n2 = 4.75 Factor a perfect square on the left side: (n + -1.5)(n + -1.5) = 4.75 Calculate the square root of the right side: 2.179449472 Break this problem into two subproblems by setting (n + -1.5) equal to 2.179449472 and -2.179449472.Subproblem 1
n + -1.5 = 2.179449472 Simplifying n + -1.5 = 2.179449472 Reorder the terms: -1.5 + n = 2.179449472 Solving -1.5 + n = 2.179449472 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = 2.179449472 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = 2.179449472 + 1.5 n = 2.179449472 + 1.5 Combine like terms: 2.179449472 + 1.5 = 3.679449472 n = 3.679449472 Simplifying n = 3.679449472Subproblem 2
n + -1.5 = -2.179449472 Simplifying n + -1.5 = -2.179449472 Reorder the terms: -1.5 + n = -2.179449472 Solving -1.5 + n = -2.179449472 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = -2.179449472 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = -2.179449472 + 1.5 n = -2.179449472 + 1.5 Combine like terms: -2.179449472 + 1.5 = -0.679449472 n = -0.679449472 Simplifying n = -0.679449472Solution
The solution to the problem is based on the solutions from the subproblems. n = {3.679449472, -0.679449472}
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