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Simplifying 8n + 8 = n2 + 4n Reorder the terms: 8 + 8n = n2 + 4n Reorder the terms: 8 + 8n = 4n + n2 Solving 8 + 8n = 4n + n2 Solving for variable 'n'. Combine like terms: 8n + -4n = 4n 8 + 4n + -1n2 = 4n + n2 + -4n + -1n2 Reorder the terms: 8 + 4n + -1n2 = 4n + -4n + n2 + -1n2 Combine like terms: 4n + -4n = 0 8 + 4n + -1n2 = 0 + n2 + -1n2 8 + 4n + -1n2 = n2 + -1n2 Combine like terms: n2 + -1n2 = 0 8 + 4n + -1n2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -8 + -4n + n2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -4n + 8 + n2 = 0 + 8 Reorder the terms: -8 + 8 + -4n + n2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -4n + n2 = 0 + 8 -4n + n2 = 0 + 8 Combine like terms: 0 + 8 = 8 -4n + n2 = 8 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 = 8 + 4 Reorder the terms: 4 + -4n + n2 = 8 + 4 Combine like terms: 8 + 4 = 12 4 + -4n + n2 = 12 Factor a perfect square on the left side: (n + -2)(n + -2) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (n + -2) equal to 3.464101615 and -3.464101615.Subproblem 1
n + -2 = 3.464101615 Simplifying n + -2 = 3.464101615 Reorder the terms: -2 + n = 3.464101615 Solving -2 + n = 3.464101615 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 = 3.464101615 + 2 Combine like terms: -2 + 2 = 0 0 + n = 3.464101615 + 2 n = 3.464101615 + 2 Combine like terms: 3.464101615 + 2 = 5.464101615 n = 5.464101615 Simplifying n = 5.464101615Subproblem 2
n + -2 = -3.464101615 Simplifying n + -2 = -3.464101615 Reorder the terms: -2 + n = -3.464101615 Solving -2 + n = -3.464101615 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 = -3.464101615 + 2 Combine like terms: -2 + 2 = 0 0 + n = -3.464101615 + 2 n = -3.464101615 + 2 Combine like terms: -3.464101615 + 2 = -1.464101615 n = -1.464101615 Simplifying n = -1.464101615Solution
The solution to the problem is based on the solutions from the subproblems. n = {5.464101615, -1.464101615}
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