n^2-4n-85=0

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Solution for n^2-4n-85=0 equation:


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 = 11.433981132

Subproblem 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 = -7.433981132

Solution

The solution to the problem is based on the solutions from the subproblems. n = {11.433981132, -7.433981132}

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