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Simplifying n2 + -4n + -85 = 0 Reorder the terms: -85 + -4n + n2 = 0 Solving -85 + -4n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '85' to each side of the equation. -85 + -4n + 85 + n2 = 0 + 85 Reorder the terms: -85 + 85 + -4n + n2 = 0 + 85 Combine like terms: -85 + 85 = 0 0 + -4n + n2 = 0 + 85 -4n + n2 = 0 + 85 Combine like terms: 0 + 85 = 85 -4n + n2 = 85 The n term is -4n. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4n + 4 + n2 = 85 + 4 Reorder the terms: 4 + -4n + n2 = 85 + 4 Combine like terms: 85 + 4 = 89 4 + -4n + n2 = 89 Factor a perfect square on the left side: (n + -2)(n + -2) = 89 Calculate the square root of the right side: 9.433981132 Break this problem into two subproblems by setting (n + -2) equal to 9.433981132 and -9.433981132.Subproblem 1
n + -2 = 9.433981132 Simplifying n + -2 = 9.433981132 Reorder the terms: -2 + n = 9.433981132 Solving -2 + n = 9.433981132 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + n = 9.433981132 + 2 Combine like terms: -2 + 2 = 0 0 + n = 9.433981132 + 2 n = 9.433981132 + 2 Combine like terms: 9.433981132 + 2 = 11.433981132 n = 11.433981132 Simplifying n = 11.433981132Subproblem 2
n + -2 = -9.433981132 Simplifying n + -2 = -9.433981132 Reorder the terms: -2 + n = -9.433981132 Solving -2 + n = -9.433981132 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + n = -9.433981132 + 2 Combine like terms: -2 + 2 = 0 0 + n = -9.433981132 + 2 n = -9.433981132 + 2 Combine like terms: -9.433981132 + 2 = -7.433981132 n = -7.433981132 Simplifying n = -7.433981132Solution
The solution to the problem is based on the solutions from the subproblems. n = {11.433981132, -7.433981132}
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