=.2x^2-2.4x+.2

Solution for =.2x^2-2.4x+.2 equation:

Simplifying
0 = 0.2x2 + -2.4x + 0.2

Reorder the terms:
0 = 0.2 + -2.4x + 0.2x2

Solving
0 = 0.2 + -2.4x + 0.2x2

Solving for variable 'x'.

Combine like terms: 0 + -0.2 = -0.2
-0.2 + 2.4x + -0.2x2 = 0.2 + -2.4x + 0.2x2 + -0.2 + 2.4x + -0.2x2

Reorder the terms:
-0.2 + 2.4x + -0.2x2 = 0.2 + -0.2 + -2.4x + 2.4x + 0.2x2 + -0.2x2

Combine like terms: 0.2 + -0.2 = 0.0
-0.2 + 2.4x + -0.2x2 = 0.0 + -2.4x + 2.4x + 0.2x2 + -0.2x2
-0.2 + 2.4x + -0.2x2 = -2.4x + 2.4x + 0.2x2 + -0.2x2

Combine like terms: -2.4x + 2.4x = 0.0
-0.2 + 2.4x + -0.2x2 = 0.0 + 0.2x2 + -0.2x2
-0.2 + 2.4x + -0.2x2 = 0.2x2 + -0.2x2

Combine like terms: 0.2x2 + -0.2x2 = 0.0
-0.2 + 2.4x + -0.2x2 = 0.0

Begin completing the square.  Divide all terms by
-0.2 the coefficient of the squared term: 

Divide each side by '-0.2'.
1 + -12x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -12x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -12x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -12x + x2 = 0 + -1
-12x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-12x + x2 = -1

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = -1 + 36

Reorder the terms:
36 + -12x + x2 = -1 + 36

Combine like terms: -1 + 36 = 35
36 + -12x + x2 = 35

Factor a perfect square on the left side:
(x + -6)(x + -6) = 35

Calculate the square root of the right side: 5.916079783

Break this problem into two subproblems by setting 
(x + -6) equal to 5.916079783 and -5.916079783.

Subproblem 1
x + -6 = 5.916079783

Simplifying
x + -6 = 5.916079783

Reorder the terms:
-6 + x = 5.916079783

Solving
-6 + x = 5.916079783

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = 5.916079783 + 6

Combine like terms: -6 + 6 = 0
0 + x = 5.916079783 + 6
x = 5.916079783 + 6

Combine like terms: 5.916079783 + 6 = 11.916079783
x = 11.916079783

Simplifying
x = 11.916079783

Subproblem 2
x + -6 = -5.916079783

Simplifying
x + -6 = -5.916079783

Reorder the terms:
-6 + x = -5.916079783

Solving
-6 + x = -5.916079783

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = -5.916079783 + 6

Combine like terms: -6 + 6 = 0
0 + x = -5.916079783 + 6
x = -5.916079783 + 6

Combine like terms: -5.916079783 + 6 = 0.083920217
x = 0.083920217

Simplifying
x = 0.083920217

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.916079783, 0.083920217}