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Simplifying 2n2 + -12n + -7 = 0 Reorder the terms: -7 + -12n + 2n2 = 0 Solving -7 + -12n + 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'. -3.5 + -6n + n2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -6n + 3.5 + n2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -6n + n2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -6n + n2 = 0 + 3.5 -6n + n2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -6n + n2 = 3.5 The n term is -6n. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6n + 9 + n2 = 3.5 + 9 Reorder the terms: 9 + -6n + n2 = 3.5 + 9 Combine like terms: 3.5 + 9 = 12.5 9 + -6n + n2 = 12.5 Factor a perfect square on the left side: (n + -3)(n + -3) = 12.5 Calculate the square root of the right side: 3.535533906 Break this problem into two subproblems by setting (n + -3) equal to 3.535533906 and -3.535533906.Subproblem 1
n + -3 = 3.535533906 Simplifying n + -3 = 3.535533906 Reorder the terms: -3 + n = 3.535533906 Solving -3 + n = 3.535533906 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + n = 3.535533906 + 3 Combine like terms: -3 + 3 = 0 0 + n = 3.535533906 + 3 n = 3.535533906 + 3 Combine like terms: 3.535533906 + 3 = 6.535533906 n = 6.535533906 Simplifying n = 6.535533906Subproblem 2
n + -3 = -3.535533906 Simplifying n + -3 = -3.535533906 Reorder the terms: -3 + n = -3.535533906 Solving -3 + n = -3.535533906 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + n = -3.535533906 + 3 Combine like terms: -3 + 3 = 0 0 + n = -3.535533906 + 3 n = -3.535533906 + 3 Combine like terms: -3.535533906 + 3 = -0.535533906 n = -0.535533906 Simplifying n = -0.535533906Solution
The solution to the problem is based on the solutions from the subproblems. n = {6.535533906, -0.535533906}
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