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Simplifying n2 + 6n = 3 Reorder the terms: 6n + n2 = 3 Solving 6n + n2 = 3 Solving for variable 'n'. Reorder the terms: -3 + 6n + n2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 6n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 6n + 3 + n2 = 0 + 3 Reorder the terms: -3 + 3 + 6n + n2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 6n + n2 = 0 + 3 6n + n2 = 0 + 3 Combine like terms: 0 + 3 = 3 6n + n2 = 3 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 + 9 Reorder the terms: 9 + 6n + n2 = 3 + 9 Combine like terms: 3 + 9 = 12 9 + 6n + n2 = 12 Factor a perfect square on the left side: (n + 3)(n + 3) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (n + 3) equal to 3.464101615 and -3.464101615.Subproblem 1
n + 3 = 3.464101615 Simplifying n + 3 = 3.464101615 Reorder the terms: 3 + n = 3.464101615 Solving 3 + n = 3.464101615 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 = 3.464101615 + -3 Combine like terms: 3 + -3 = 0 0 + n = 3.464101615 + -3 n = 3.464101615 + -3 Combine like terms: 3.464101615 + -3 = 0.464101615 n = 0.464101615 Simplifying n = 0.464101615Subproblem 2
n + 3 = -3.464101615 Simplifying n + 3 = -3.464101615 Reorder the terms: 3 + n = -3.464101615 Solving 3 + n = -3.464101615 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 = -3.464101615 + -3 Combine like terms: 3 + -3 = 0 0 + n = -3.464101615 + -3 n = -3.464101615 + -3 Combine like terms: -3.464101615 + -3 = -6.464101615 n = -6.464101615 Simplifying n = -6.464101615Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.464101615, -6.464101615}
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