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Simplifying n2 + -6n = 1 Reorder the terms: -6n + n2 = 1 Solving -6n + n2 = 1 Solving for variable 'n'. Reorder the terms: -1 + -6n + n2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -6n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -6n + 1 + n2 = 0 + 1 Reorder the terms: -1 + 1 + -6n + n2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -6n + n2 = 0 + 1 -6n + n2 = 0 + 1 Combine like terms: 0 + 1 = 1 -6n + n2 = 1 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 = 1 + 9 Reorder the terms: 9 + -6n + n2 = 1 + 9 Combine like terms: 1 + 9 = 10 9 + -6n + n2 = 10 Factor a perfect square on the left side: (n + -3)(n + -3) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (n + -3) equal to 3.16227766 and -3.16227766.Subproblem 1
n + -3 = 3.16227766 Simplifying n + -3 = 3.16227766 Reorder the terms: -3 + n = 3.16227766 Solving -3 + n = 3.16227766 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 = 3.16227766 + 3 Combine like terms: -3 + 3 = 0 0 + n = 3.16227766 + 3 n = 3.16227766 + 3 Combine like terms: 3.16227766 + 3 = 6.16227766 n = 6.16227766 Simplifying n = 6.16227766Subproblem 2
n + -3 = -3.16227766 Simplifying n + -3 = -3.16227766 Reorder the terms: -3 + n = -3.16227766 Solving -3 + n = -3.16227766 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 = -3.16227766 + 3 Combine like terms: -3 + 3 = 0 0 + n = -3.16227766 + 3 n = -3.16227766 + 3 Combine like terms: -3.16227766 + 3 = -0.16227766 n = -0.16227766 Simplifying n = -0.16227766Solution
The solution to the problem is based on the solutions from the subproblems. n = {6.16227766, -0.16227766}
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