9n^2-50n-80=0

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Solution for 9n^2-50n-80=0 equation: 


Simplifying
9n2 + -50n + -80 = 0

Reorder the terms:
-80 + -50n + 9n2 = 0

Solving
-80 + -50n + 9n2 = 0

Solving for variable 'n'.

Begin completing the square.  Divide all terms by
9 the coefficient of the squared term: 

Divide each side by '9'.
-8.888888889 + -5.555555556n + n2 = 0

Move the constant term to the right:

Add '8.888888889' to each side of the equation.
-8.888888889 + -5.555555556n + 8.888888889 + n2 = 0 + 8.888888889

Reorder the terms:
-8.888888889 + 8.888888889 + -5.555555556n + n2 = 0 + 8.888888889

Combine like terms: -8.888888889 + 8.888888889 = 0.000000000
0.000000000 + -5.555555556n + n2 = 0 + 8.888888889
-5.555555556n + n2 = 0 + 8.888888889

Combine like terms: 0 + 8.888888889 = 8.888888889
-5.555555556n + n2 = 8.888888889

The n term is -5.555555556n.  Take half its coefficient (-2.777777778).
Square it (7.716049384) and add it to both sides.

Add '7.716049384' to each side of the equation.
-5.555555556n + 7.716049384 + n2 = 8.888888889 + 7.716049384

Reorder the terms:
7.716049384 + -5.555555556n + n2 = 8.888888889 + 7.716049384

Combine like terms: 8.888888889 + 7.716049384 = 16.604938273
7.716049384 + -5.555555556n + n2 = 16.604938273

Factor a perfect square on the left side:
(n + -2.777777778)(n + -2.777777778) = 16.604938273

Calculate the square root of the right side: 4.074915738

Break this problem into two subproblems by setting 
(n + -2.777777778) equal to 4.074915738 and -4.074915738.


Subproblem 1
n + -2.777777778 = 4.074915738

Simplifying
n + -2.777777778 = 4.074915738

Reorder the terms:
-2.777777778 + n = 4.074915738

Solving
-2.777777778 + n = 4.074915738

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '2.777777778' to each side of the equation.
-2.777777778 + 2.777777778 + n = 4.074915738 + 2.777777778

Combine like terms: -2.777777778 + 2.777777778 = 0.000000000
0.000000000 + n = 4.074915738 + 2.777777778
n = 4.074915738 + 2.777777778

Combine like terms: 4.074915738 + 2.777777778 = 6.852693516
n = 6.852693516

Simplifying
n = 6.852693516


Subproblem 2
n + -2.777777778 = -4.074915738

Simplifying
n + -2.777777778 = -4.074915738

Reorder the terms:
-2.777777778 + n = -4.074915738

Solving
-2.777777778 + n = -4.074915738

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '2.777777778' to each side of the equation.
-2.777777778 + 2.777777778 + n = -4.074915738 + 2.777777778

Combine like terms: -2.777777778 + 2.777777778 = 0.000000000
0.000000000 + n = -4.074915738 + 2.777777778
n = -4.074915738 + 2.777777778

Combine like terms: -4.074915738 + 2.777777778 = -1.29713796
n = -1.29713796

Simplifying
n = -1.29713796


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {6.852693516, -1.29713796}

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