-9x^2+8x-1=0

Solution for -9x^2+8x-1=0 equation:

Simplifying
-9x2 + 8x + -1 = 0

Reorder the terms:
-1 + 8x + -9x2 = 0

Solving
-1 + 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'.
0.1111111111 + -0.8888888889x + x2 = 0

Move the constant term to the right:

Add '-0.1111111111' to each side of the equation.
0.1111111111 + -0.8888888889x + -0.1111111111 + x2 = 0 + -0.1111111111

Reorder the terms:
0.1111111111 + -0.1111111111 + -0.8888888889x + x2 = 0 + -0.1111111111

Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000
0.0000000000 + -0.8888888889x + x2 = 0 + -0.1111111111
-0.8888888889x + x2 = 0 + -0.1111111111

Combine like terms: 0 + -0.1111111111 = -0.1111111111
-0.8888888889x + x2 = -0.1111111111

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 = -0.1111111111 + 0.1975308642

Reorder the terms:
0.1975308642 + -0.8888888889x + x2 = -0.1111111111 + 0.1975308642

Combine like terms: -0.1111111111 + 0.1975308642 = 0.0864197531
0.1975308642 + -0.8888888889x + x2 = 0.0864197531

Factor a perfect square on the left side:
(x + -0.4444444445)(x + -0.4444444445) = 0.0864197531

Calculate the square root of the right side: 0.293972368

Break this problem into two subproblems by setting 
(x + -0.4444444445) equal to 0.293972368 and -0.293972368.

Subproblem 1
x + -0.4444444445 = 0.293972368

Simplifying
x + -0.4444444445 = 0.293972368

Reorder the terms:
-0.4444444445 + x = 0.293972368

Solving
-0.4444444445 + x = 0.293972368

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 = 0.293972368 + 0.4444444445

Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000
0.0000000000 + x = 0.293972368 + 0.4444444445
x = 0.293972368 + 0.4444444445

Combine like terms: 0.293972368 + 0.4444444445 = 0.7384168125
x = 0.7384168125

Simplifying
x = 0.7384168125

Subproblem 2
x + -0.4444444445 = -0.293972368

Simplifying
x + -0.4444444445 = -0.293972368

Reorder the terms:
-0.4444444445 + x = -0.293972368

Solving
-0.4444444445 + x = -0.293972368

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 = -0.293972368 + 0.4444444445

Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000
0.0000000000 + x = -0.293972368 + 0.4444444445
x = -0.293972368 + 0.4444444445

Combine like terms: -0.293972368 + 0.4444444445 = 0.1504720765
x = 0.1504720765

Simplifying
x = 0.1504720765

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.7384168125, 0.1504720765}