9x^2-9x-5=0

Solution for 9x^2-9x-5=0 equation:

Simplifying
9x2 + -9x + -5 = 0

Reorder the terms:
-5 + -9x + 9x2 = 0

Solving
-5 + -9x + 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'.
-0.5555555556 + -1x + x2 = 0

Move the constant term to the right:

Add '0.5555555556' to each side of the equation.
-0.5555555556 + -1x + 0.5555555556 + x2 = 0 + 0.5555555556

Reorder the terms:
-0.5555555556 + 0.5555555556 + -1x + x2 = 0 + 0.5555555556

Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000
0.0000000000 + -1x + x2 = 0 + 0.5555555556
-1x + x2 = 0 + 0.5555555556

Combine like terms: 0 + 0.5555555556 = 0.5555555556
-1x + x2 = 0.5555555556

The x term is -1x.  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.
-1x + 0.25 + x2 = 0.5555555556 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 0.5555555556 + 0.25

Combine like terms: 0.5555555556 + 0.25 = 0.8055555556
0.25 + -1x + x2 = 0.8055555556

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 0.8055555556

Calculate the square root of the right side: 0.897527468

Break this problem into two subproblems by setting 
(x + -0.5) equal to 0.897527468 and -0.897527468.

Subproblem 1
x + -0.5 = 0.897527468

Simplifying
x + -0.5 = 0.897527468

Reorder the terms:
-0.5 + x = 0.897527468

Solving
-0.5 + x = 0.897527468

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 0.897527468 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 0.897527468 + 0.5
x = 0.897527468 + 0.5

Combine like terms: 0.897527468 + 0.5 = 1.397527468
x = 1.397527468

Simplifying
x = 1.397527468

Subproblem 2
x + -0.5 = -0.897527468

Simplifying
x + -0.5 = -0.897527468

Reorder the terms:
-0.5 + x = -0.897527468

Solving
-0.5 + x = -0.897527468

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -0.897527468 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -0.897527468 + 0.5
x = -0.897527468 + 0.5

Combine like terms: -0.897527468 + 0.5 = -0.397527468
x = -0.397527468

Simplifying
x = -0.397527468

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.397527468, -0.397527468}