9x^2+9x-8=0

Solution for 9x^2+9x-8=0 equation:

Simplifying
9x2 + 9x + -8 = 0

Reorder the terms:
-8 + 9x + 9x2 = 0

Solving
-8 + 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'.
-0.8888888889 + x + x2 = 0

Move the constant term to the right:

Add '0.8888888889' to each side of the equation.
-0.8888888889 + x + 0.8888888889 + x2 = 0 + 0.8888888889

Reorder the terms:
-0.8888888889 + 0.8888888889 + x + x2 = 0 + 0.8888888889

Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000
0.0000000000 + x + x2 = 0 + 0.8888888889
x + x2 = 0 + 0.8888888889

Combine like terms: 0 + 0.8888888889 = 0.8888888889
x + x2 = 0.8888888889

The x term is x.  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.
 + 0.25 + x2 = 0.8888888889 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 0.8888888889 + 0.25

Combine like terms: 0.8888888889 + 0.25 = 1.1388888889
1.25 + x2 = 1.1388888889

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 1.1388888889

Calculate the square root of the right side: 1.067187373

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.067187373 and -1.067187373.

Subproblem 1
x + 0.5 = 1.067187373

Simplifying
x + 0.5 = 1.067187373

Reorder the terms:
0.5 + x = 1.067187373

Solving
0.5 + x = 1.067187373

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 = 1.067187373 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.067187373 + -0.5
x = 1.067187373 + -0.5

Combine like terms: 1.067187373 + -0.5 = 0.567187373
x = 0.567187373

Simplifying
x = 0.567187373

Subproblem 2
x + 0.5 = -1.067187373

Simplifying
x + 0.5 = -1.067187373

Reorder the terms:
0.5 + x = -1.067187373

Solving
0.5 + x = -1.067187373

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 = -1.067187373 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.067187373 + -0.5
x = -1.067187373 + -0.5

Combine like terms: -1.067187373 + -0.5 = -1.567187373
x = -1.567187373

Simplifying
x = -1.567187373

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.567187373, -1.567187373}