9x^2-640x-5500=0

Solution for 9x^2-640x-5500=0 equation:

Simplifying
9x2 + -640x + -5500 = 0

Reorder the terms:
-5500 + -640x + 9x2 = 0

Solving
-5500 + -640x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
-611.1111111 + -71.11111111x + x2 = 0

Move the constant term to the right:

Add '611.1111111' to each side of the equation.
-611.1111111 + -71.11111111x + 611.1111111 + x2 = 0 + 611.1111111

Reorder the terms:
-611.1111111 + 611.1111111 + -71.11111111x + x2 = 0 + 611.1111111

Combine like terms: -611.1111111 + 611.1111111 = 0.0000000
0.0000000 + -71.11111111x + x2 = 0 + 611.1111111
-71.11111111x + x2 = 0 + 611.1111111

Combine like terms: 0 + 611.1111111 = 611.1111111
-71.11111111x + x2 = 611.1111111

The x term is -71.11111111x.  Take half its coefficient (-35.55555556).
Square it (1264.197531) and add it to both sides.

Add '1264.197531' to each side of the equation.
-71.11111111x + 1264.197531 + x2 = 611.1111111 + 1264.197531

Reorder the terms:
1264.197531 + -71.11111111x + x2 = 611.1111111 + 1264.197531

Combine like terms: 611.1111111 + 1264.197531 = 1875.3086421
1264.197531 + -71.11111111x + x2 = 1875.3086421

Factor a perfect square on the left side:
(x + -35.55555556)(x + -35.55555556) = 1875.3086421

Calculate the square root of the right side: 43.304833935

Break this problem into two subproblems by setting 
(x + -35.55555556) equal to 43.304833935 and -43.304833935.

Subproblem 1
x + -35.55555556 = 43.304833935

Simplifying
x + -35.55555556 = 43.304833935

Reorder the terms:
-35.55555556 + x = 43.304833935

Solving
-35.55555556 + x = 43.304833935

Solving for variable 'x'.

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

Add '35.55555556' to each side of the equation.
-35.55555556 + 35.55555556 + x = 43.304833935 + 35.55555556

Combine like terms: -35.55555556 + 35.55555556 = 0.00000000
0.00000000 + x = 43.304833935 + 35.55555556
x = 43.304833935 + 35.55555556

Combine like terms: 43.304833935 + 35.55555556 = 78.860389495
x = 78.860389495

Simplifying
x = 78.860389495

Subproblem 2
x + -35.55555556 = -43.304833935

Simplifying
x + -35.55555556 = -43.304833935

Reorder the terms:
-35.55555556 + x = -43.304833935

Solving
-35.55555556 + x = -43.304833935

Solving for variable 'x'.

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

Add '35.55555556' to each side of the equation.
-35.55555556 + 35.55555556 + x = -43.304833935 + 35.55555556

Combine like terms: -35.55555556 + 35.55555556 = 0.00000000
0.00000000 + x = -43.304833935 + 35.55555556
x = -43.304833935 + 35.55555556

Combine like terms: -43.304833935 + 35.55555556 = -7.749278375
x = -7.749278375

Simplifying
x = -7.749278375

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {78.860389495, -7.749278375}