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Simplifying 3n2 + -7 + -18n = 0 Reorder the terms: -7 + -18n + 3n2 = 0 Solving -7 + -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'. -2.333333333 + -6n + n2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + -6n + 2.333333333 + n2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + -6n + n2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + -6n + n2 = 0 + 2.333333333 -6n + n2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 -6n + n2 = 2.333333333 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 = 2.333333333 + 9 Reorder the terms: 9 + -6n + n2 = 2.333333333 + 9 Combine like terms: 2.333333333 + 9 = 11.333333333 9 + -6n + n2 = 11.333333333 Factor a perfect square on the left side: (n + -3)(n + -3) = 11.333333333 Calculate the square root of the right side: 3.366501646 Break this problem into two subproblems by setting (n + -3) equal to 3.366501646 and -3.366501646.Subproblem 1
n + -3 = 3.366501646 Simplifying n + -3 = 3.366501646 Reorder the terms: -3 + n = 3.366501646 Solving -3 + n = 3.366501646 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 = 3.366501646 + 3 Combine like terms: -3 + 3 = 0 0 + n = 3.366501646 + 3 n = 3.366501646 + 3 Combine like terms: 3.366501646 + 3 = 6.366501646 n = 6.366501646 Simplifying n = 6.366501646Subproblem 2
n + -3 = -3.366501646 Simplifying n + -3 = -3.366501646 Reorder the terms: -3 + n = -3.366501646 Solving -3 + n = -3.366501646 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 = -3.366501646 + 3 Combine like terms: -3 + 3 = 0 0 + n = -3.366501646 + 3 n = -3.366501646 + 3 Combine like terms: -3.366501646 + 3 = -0.366501646 n = -0.366501646 Simplifying n = -0.366501646Solution
The solution to the problem is based on the solutions from the subproblems. n = {6.366501646, -0.366501646}
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