a^2-111a-2160=0

Solution for a^2-111a-2160=0 equation:

Simplifying
a2 + -111a + -2160 = 0

Reorder the terms:
-2160 + -111a + a2 = 0

Solving
-2160 + -111a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '2160' to each side of the equation.
-2160 + -111a + 2160 + a2 = 0 + 2160

Reorder the terms:
-2160 + 2160 + -111a + a2 = 0 + 2160

Combine like terms: -2160 + 2160 = 0
0 + -111a + a2 = 0 + 2160
-111a + a2 = 0 + 2160

Combine like terms: 0 + 2160 = 2160
-111a + a2 = 2160

The a term is -111a.  Take half its coefficient (-55.5).
Square it (3080.25) and add it to both sides.

Add '3080.25' to each side of the equation.
-111a + 3080.25 + a2 = 2160 + 3080.25

Reorder the terms:
3080.25 + -111a + a2 = 2160 + 3080.25

Combine like terms: 2160 + 3080.25 = 5240.25
3080.25 + -111a + a2 = 5240.25

Factor a perfect square on the left side:
(a + -55.5)(a + -55.5) = 5240.25

Calculate the square root of the right side: 72.389571072

Break this problem into two subproblems by setting 
(a + -55.5) equal to 72.389571072 and -72.389571072.

Subproblem 1
a + -55.5 = 72.389571072

Simplifying
a + -55.5 = 72.389571072

Reorder the terms:
-55.5 + a = 72.389571072

Solving
-55.5 + a = 72.389571072

Solving for variable 'a'.

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

Add '55.5' to each side of the equation.
-55.5 + 55.5 + a = 72.389571072 + 55.5

Combine like terms: -55.5 + 55.5 = 0.0
0.0 + a = 72.389571072 + 55.5
a = 72.389571072 + 55.5

Combine like terms: 72.389571072 + 55.5 = 127.889571072
a = 127.889571072

Simplifying
a = 127.889571072

Subproblem 2
a + -55.5 = -72.389571072

Simplifying
a + -55.5 = -72.389571072

Reorder the terms:
-55.5 + a = -72.389571072

Solving
-55.5 + a = -72.389571072

Solving for variable 'a'.

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

Add '55.5' to each side of the equation.
-55.5 + 55.5 + a = -72.389571072 + 55.5

Combine like terms: -55.5 + 55.5 = 0.0
0.0 + a = -72.389571072 + 55.5
a = -72.389571072 + 55.5

Combine like terms: -72.389571072 + 55.5 = -16.889571072
a = -16.889571072

Simplifying
a = -16.889571072

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {127.889571072, -16.889571072}