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Simplifying n2 + -6n = 28 Reorder the terms: -6n + n2 = 28 Solving -6n + n2 = 28 Solving for variable 'n'. Reorder the terms: -28 + -6n + n2 = 28 + -28 Combine like terms: 28 + -28 = 0 -28 + -6n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + -6n + 28 + n2 = 0 + 28 Reorder the terms: -28 + 28 + -6n + n2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -6n + n2 = 0 + 28 -6n + n2 = 0 + 28 Combine like terms: 0 + 28 = 28 -6n + n2 = 28 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 = 28 + 9 Reorder the terms: 9 + -6n + n2 = 28 + 9 Combine like terms: 28 + 9 = 37 9 + -6n + n2 = 37 Factor a perfect square on the left side: (n + -3)(n + -3) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (n + -3) equal to 6.08276253 and -6.08276253.Subproblem 1
n + -3 = 6.08276253 Simplifying n + -3 = 6.08276253 Reorder the terms: -3 + n = 6.08276253 Solving -3 + n = 6.08276253 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 = 6.08276253 + 3 Combine like terms: -3 + 3 = 0 0 + n = 6.08276253 + 3 n = 6.08276253 + 3 Combine like terms: 6.08276253 + 3 = 9.08276253 n = 9.08276253 Simplifying n = 9.08276253Subproblem 2
n + -3 = -6.08276253 Simplifying n + -3 = -6.08276253 Reorder the terms: -3 + n = -6.08276253 Solving -3 + n = -6.08276253 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 = -6.08276253 + 3 Combine like terms: -3 + 3 = 0 0 + n = -6.08276253 + 3 n = -6.08276253 + 3 Combine like terms: -6.08276253 + 3 = -3.08276253 n = -3.08276253 Simplifying n = -3.08276253Solution
The solution to the problem is based on the solutions from the subproblems. n = {9.08276253, -3.08276253}
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