33x^2-6x+0.25=0

Solution for 33x^2-6x+0.25=0 equation:

Simplifying
33x2 + -6x + 0.25 = 0

Reorder the terms:
0.25 + -6x + 33x2 = 0

Solving
0.25 + -6x + 33x2 = 0

Solving for variable 'x'.

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

Divide each side by '33'.
0.007575757576 + -0.1818181818x + x2 = 0

Move the constant term to the right:

Add '-0.007575757576' to each side of the equation.
0.007575757576 + -0.1818181818x + -0.007575757576 + x2 = 0 + -0.007575757576

Reorder the terms:
0.007575757576 + -0.007575757576 + -0.1818181818x + x2 = 0 + -0.007575757576

Combine like terms: 0.007575757576 + -0.007575757576 = 0.000000000000
0.000000000000 + -0.1818181818x + x2 = 0 + -0.007575757576
-0.1818181818x + x2 = 0 + -0.007575757576

Combine like terms: 0 + -0.007575757576 = -0.007575757576
-0.1818181818x + x2 = -0.007575757576

The x term is -0.1818181818x.  Take half its coefficient (-0.0909090909).
Square it (0.008264462808) and add it to both sides.

Add '0.008264462808' to each side of the equation.
-0.1818181818x + 0.008264462808 + x2 = -0.007575757576 + 0.008264462808

Reorder the terms:
0.008264462808 + -0.1818181818x + x2 = -0.007575757576 + 0.008264462808

Combine like terms: -0.007575757576 + 0.008264462808 = 0.000688705232
0.008264462808 + -0.1818181818x + x2 = 0.000688705232

Factor a perfect square on the left side:
(x + -0.0909090909)(x + -0.0909090909) = 0.000688705232

Calculate the square root of the right side: 0.026243194

Break this problem into two subproblems by setting 
(x + -0.0909090909) equal to 0.026243194 and -0.026243194.

Subproblem 1
x + -0.0909090909 = 0.026243194

Simplifying
x + -0.0909090909 = 0.026243194

Reorder the terms:
-0.0909090909 + x = 0.026243194

Solving
-0.0909090909 + x = 0.026243194

Solving for variable 'x'.

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

Add '0.0909090909' to each side of the equation.
-0.0909090909 + 0.0909090909 + x = 0.026243194 + 0.0909090909

Combine like terms: -0.0909090909 + 0.0909090909 = 0.0000000000
0.0000000000 + x = 0.026243194 + 0.0909090909
x = 0.026243194 + 0.0909090909

Combine like terms: 0.026243194 + 0.0909090909 = 0.1171522849
x = 0.1171522849

Simplifying
x = 0.1171522849

Subproblem 2
x + -0.0909090909 = -0.026243194

Simplifying
x + -0.0909090909 = -0.026243194

Reorder the terms:
-0.0909090909 + x = -0.026243194

Solving
-0.0909090909 + x = -0.026243194

Solving for variable 'x'.

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

Add '0.0909090909' to each side of the equation.
-0.0909090909 + 0.0909090909 + x = -0.026243194 + 0.0909090909

Combine like terms: -0.0909090909 + 0.0909090909 = 0.0000000000
0.0000000000 + x = -0.026243194 + 0.0909090909
x = -0.026243194 + 0.0909090909

Combine like terms: -0.026243194 + 0.0909090909 = 0.0646658969
x = 0.0646658969

Simplifying
x = 0.0646658969

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.1171522849, 0.0646658969}