n^2-n-160=0

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Solution for n^2-n-160=0 equation:


Simplifying
n2 + -1n + -160 = 0

Reorder the terms:
-160 + -1n + n2 = 0

Solving
-160 + -1n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '160' to each side of the equation.
-160 + -1n + 160 + n2 = 0 + 160

Reorder the terms:
-160 + 160 + -1n + n2 = 0 + 160

Combine like terms: -160 + 160 = 0
0 + -1n + n2 = 0 + 160
-1n + n2 = 0 + 160

Combine like terms: 0 + 160 = 160
-1n + n2 = 160

The n term is -1n.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1n + 0.25 + n2 = 160 + 0.25

Reorder the terms:
0.25 + -1n + n2 = 160 + 0.25

Combine like terms: 160 + 0.25 = 160.25
0.25 + -1n + n2 = 160.25

Factor a perfect square on the left side:
(n + -0.5)(n + -0.5) = 160.25

Calculate the square root of the right side: 12.658988901

Break this problem into two subproblems by setting 
(n + -0.5) equal to 12.658988901 and -12.658988901.

Subproblem 1

n + -0.5 = 12.658988901 Simplifying n + -0.5 = 12.658988901 Reorder the terms: -0.5 + n = 12.658988901 Solving -0.5 + n = 12.658988901 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + n = 12.658988901 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = 12.658988901 + 0.5 n = 12.658988901 + 0.5 Combine like terms: 12.658988901 + 0.5 = 13.158988901 n = 13.158988901 Simplifying n = 13.158988901

Subproblem 2

n + -0.5 = -12.658988901 Simplifying n + -0.5 = -12.658988901 Reorder the terms: -0.5 + n = -12.658988901 Solving -0.5 + n = -12.658988901 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + n = -12.658988901 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = -12.658988901 + 0.5 n = -12.658988901 + 0.5 Combine like terms: -12.658988901 + 0.5 = -12.158988901 n = -12.158988901 Simplifying n = -12.158988901

Solution

The solution to the problem is based on the solutions from the subproblems. n = {13.158988901, -12.158988901}

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