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Simplifying n2 + -6n + -3 = 0 Reorder the terms: -3 + -6n + n2 = 0 Solving -3 + -6n + n2 = 0 Solving for variable 'n'. 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 = 6.464101615 n = 6.464101615 Simplifying n = 6.464101615Subproblem 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 = -0.464101615 n = -0.464101615 Simplifying n = -0.464101615Solution
The solution to the problem is based on the solutions from the subproblems. n = {6.464101615, -0.464101615}
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