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Simplifying n(n + -6) = 9 Reorder the terms: n(-6 + n) = 9 (-6 * n + n * n) = 9 (-6n + n2) = 9 Solving -6n + n2 = 9 Solving for variable 'n'. Reorder the terms: -9 + -6n + n2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + -6n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -6n + 9 + n2 = 0 + 9 Reorder the terms: -9 + 9 + -6n + n2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -6n + n2 = 0 + 9 -6n + n2 = 0 + 9 Combine like terms: 0 + 9 = 9 -6n + n2 = 9 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 = 9 + 9 Reorder the terms: 9 + -6n + n2 = 9 + 9 Combine like terms: 9 + 9 = 18 9 + -6n + n2 = 18 Factor a perfect square on the left side: (n + -3)(n + -3) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (n + -3) equal to 4.242640687 and -4.242640687.Subproblem 1
n + -3 = 4.242640687 Simplifying n + -3 = 4.242640687 Reorder the terms: -3 + n = 4.242640687 Solving -3 + n = 4.242640687 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 = 4.242640687 + 3 Combine like terms: -3 + 3 = 0 0 + n = 4.242640687 + 3 n = 4.242640687 + 3 Combine like terms: 4.242640687 + 3 = 7.242640687 n = 7.242640687 Simplifying n = 7.242640687Subproblem 2
n + -3 = -4.242640687 Simplifying n + -3 = -4.242640687 Reorder the terms: -3 + n = -4.242640687 Solving -3 + n = -4.242640687 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 = -4.242640687 + 3 Combine like terms: -3 + 3 = 0 0 + n = -4.242640687 + 3 n = -4.242640687 + 3 Combine like terms: -4.242640687 + 3 = -1.242640687 n = -1.242640687 Simplifying n = -1.242640687Solution
The solution to the problem is based on the solutions from the subproblems. n = {7.242640687, -1.242640687}
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