0.3x^2-0.6x+0.3=0

Solution for 0.3x^2-0.6x+0.3=0 equation:

Simplifying
0.3x2 + -0.6x + 0.3 = 0

Reorder the terms:
0.3 + -0.6x + 0.3x2 = 0

Solving
0.3 + -0.6x + 0.3x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.3'.
1 + -2x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -2x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -2x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x + x2 = 0 + -1
-2x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2x + x2 = -1

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -1 + 1

Reorder the terms:
1 + -2x + x2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + -2x + x2 = 0

Factor a perfect square on the left side:
(x + -1)(x + -1) = 0

Calculate the square root of the right side: 0

Break this problem into two subproblems by setting 
(x + -1) equal to 0 and 0.

Subproblem 1
x + -1 = 0

Simplifying
x + -1 = 0

Reorder the terms:
-1 + x = 0

Solving
-1 + x = 0

Solving for variable 'x'.

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

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

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

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

Simplifying
x = 1

Subproblem 2
x + -1 = 0

Simplifying
x + -1 = 0

Reorder the terms:
-1 + x = 0

Solving
-1 + x = 0

Solving for variable 'x'.

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

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

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

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

Simplifying
x = 1

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1, 1}