-3x^2+9x-1=0

Solution for -3x^2+9x-1=0 equation:

Simplifying
-3x2 + 9x + -1 = 0

Reorder the terms:
-1 + 9x + -3x2 = 0

Solving
-1 + 9x + -3x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
0.3333333333 + -3x + x2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + -3x + -0.3333333333 + x2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + -3x + x2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + -3x + x2 = 0 + -0.3333333333
-3x + x2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
-3x + x2 = -0.3333333333

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = -0.3333333333 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -0.3333333333 + 2.25

Combine like terms: -0.3333333333 + 2.25 = 1.9166666667
2.25 + -3x + x2 = 1.9166666667

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 1.9166666667

Calculate the square root of the right side: 1.38443731

Break this problem into two subproblems by setting 
(x + -1.5) equal to 1.38443731 and -1.38443731.

Subproblem 1
x + -1.5 = 1.38443731

Simplifying
x + -1.5 = 1.38443731

Reorder the terms:
-1.5 + x = 1.38443731

Solving
-1.5 + x = 1.38443731

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 1.38443731 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 1.38443731 + 1.5
x = 1.38443731 + 1.5

Combine like terms: 1.38443731 + 1.5 = 2.88443731
x = 2.88443731

Simplifying
x = 2.88443731

Subproblem 2
x + -1.5 = -1.38443731

Simplifying
x + -1.5 = -1.38443731

Reorder the terms:
-1.5 + x = -1.38443731

Solving
-1.5 + x = -1.38443731

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -1.38443731 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -1.38443731 + 1.5
x = -1.38443731 + 1.5

Combine like terms: -1.38443731 + 1.5 = 0.11556269
x = 0.11556269

Simplifying
x = 0.11556269

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.88443731, 0.11556269}