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Simplifying 4n2 + 16n + -8 = 3 Reorder the terms: -8 + 16n + 4n2 = 3 Solving -8 + 16n + 4n2 = 3 Solving for variable 'n'. Reorder the terms: -8 + -3 + 16n + 4n2 = 3 + -3 Combine like terms: -8 + -3 = -11 -11 + 16n + 4n2 = 3 + -3 Combine like terms: 3 + -3 = 0 -11 + 16n + 4n2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.75 + 4n + n2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + 4n + 2.75 + n2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + 4n + n2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + 4n + n2 = 0 + 2.75 4n + n2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 4n + n2 = 2.75 The n term is 4n. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4n + 4 + n2 = 2.75 + 4 Reorder the terms: 4 + 4n + n2 = 2.75 + 4 Combine like terms: 2.75 + 4 = 6.75 4 + 4n + n2 = 6.75 Factor a perfect square on the left side: (n + 2)(n + 2) = 6.75 Calculate the square root of the right side: 2.598076211 Break this problem into two subproblems by setting (n + 2) equal to 2.598076211 and -2.598076211.Subproblem 1
n + 2 = 2.598076211 Simplifying n + 2 = 2.598076211 Reorder the terms: 2 + n = 2.598076211 Solving 2 + n = 2.598076211 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + n = 2.598076211 + -2 Combine like terms: 2 + -2 = 0 0 + n = 2.598076211 + -2 n = 2.598076211 + -2 Combine like terms: 2.598076211 + -2 = 0.598076211 n = 0.598076211 Simplifying n = 0.598076211Subproblem 2
n + 2 = -2.598076211 Simplifying n + 2 = -2.598076211 Reorder the terms: 2 + n = -2.598076211 Solving 2 + n = -2.598076211 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + n = -2.598076211 + -2 Combine like terms: 2 + -2 = 0 0 + n = -2.598076211 + -2 n = -2.598076211 + -2 Combine like terms: -2.598076211 + -2 = -4.598076211 n = -4.598076211 Simplifying n = -4.598076211Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.598076211, -4.598076211}
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