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Simplifying 3n2 + -18n + -1 = 0 Reorder the terms: -1 + -18n + 3n2 = 0 Solving -1 + -18n + 3n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.3333333333 + -6n + n2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -6n + 0.3333333333 + n2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -6n + n2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -6n + n2 = 0 + 0.3333333333 -6n + n2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -6n + n2 = 0.3333333333 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 = 0.3333333333 + 9 Reorder the terms: 9 + -6n + n2 = 0.3333333333 + 9 Combine like terms: 0.3333333333 + 9 = 9.3333333333 9 + -6n + n2 = 9.3333333333 Factor a perfect square on the left side: (n + -3)(n + -3) = 9.3333333333 Calculate the square root of the right side: 3.055050463 Break this problem into two subproblems by setting (n + -3) equal to 3.055050463 and -3.055050463.Subproblem 1
n + -3 = 3.055050463 Simplifying n + -3 = 3.055050463 Reorder the terms: -3 + n = 3.055050463 Solving -3 + n = 3.055050463 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 = 3.055050463 + 3 Combine like terms: -3 + 3 = 0 0 + n = 3.055050463 + 3 n = 3.055050463 + 3 Combine like terms: 3.055050463 + 3 = 6.055050463 n = 6.055050463 Simplifying n = 6.055050463Subproblem 2
n + -3 = -3.055050463 Simplifying n + -3 = -3.055050463 Reorder the terms: -3 + n = -3.055050463 Solving -3 + n = -3.055050463 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 = -3.055050463 + 3 Combine like terms: -3 + 3 = 0 0 + n = -3.055050463 + 3 n = -3.055050463 + 3 Combine like terms: -3.055050463 + 3 = -0.055050463 n = -0.055050463 Simplifying n = -0.055050463Solution
The solution to the problem is based on the solutions from the subproblems. n = {6.055050463, -0.055050463}
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