-9x^2-8x+9=0

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

Simplifying
-9x2 + -8x + 9 = 0

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

Solving
9 + -8x + -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'.
-1 + 0.8888888889x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 0.8888888889x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 0.8888888889x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 0.8888888889x + x2 = 0 + 1
0.8888888889x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
0.8888888889x + x2 = 1

The x term is 0.8888888889x.  Take half its coefficient (0.4444444445).
Square it (0.1975308642) and add it to both sides.

Add '0.1975308642' to each side of the equation.
0.8888888889x + 0.1975308642 + x2 = 1 + 0.1975308642

Reorder the terms:
0.1975308642 + 0.8888888889x + x2 = 1 + 0.1975308642

Combine like terms: 1 + 0.1975308642 = 1.1975308642
0.1975308642 + 0.8888888889x + x2 = 1.1975308642

Factor a perfect square on the left side:
(x + 0.4444444445)(x + 0.4444444445) = 1.1975308642

Calculate the square root of the right side: 1.094317534

Break this problem into two subproblems by setting 
(x + 0.4444444445) equal to 1.094317534 and -1.094317534.

Subproblem 1
x + 0.4444444445 = 1.094317534

Simplifying
x + 0.4444444445 = 1.094317534

Reorder the terms:
0.4444444445 + x = 1.094317534

Solving
0.4444444445 + x = 1.094317534

Solving for variable 'x'.

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

Add '-0.4444444445' to each side of the equation.
0.4444444445 + -0.4444444445 + x = 1.094317534 + -0.4444444445

Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000
0.0000000000 + x = 1.094317534 + -0.4444444445
x = 1.094317534 + -0.4444444445

Combine like terms: 1.094317534 + -0.4444444445 = 0.6498730895
x = 0.6498730895

Simplifying
x = 0.6498730895

Subproblem 2
x + 0.4444444445 = -1.094317534

Simplifying
x + 0.4444444445 = -1.094317534

Reorder the terms:
0.4444444445 + x = -1.094317534

Solving
0.4444444445 + x = -1.094317534

Solving for variable 'x'.

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

Add '-0.4444444445' to each side of the equation.
0.4444444445 + -0.4444444445 + x = -1.094317534 + -0.4444444445

Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000
0.0000000000 + x = -1.094317534 + -0.4444444445
x = -1.094317534 + -0.4444444445

Combine like terms: -1.094317534 + -0.4444444445 = -1.5387619785
x = -1.5387619785

Simplifying
x = -1.5387619785

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.6498730895, -1.5387619785}