x^2-1.6*x+0.6=0

Solution for x^2-1.6*x+0.6=0 equation:

Simplifying
x2 + -1.6x + 0.6 = 0

Reorder the terms:
0.6 + -1.6x + x2 = 0

Solving
0.6 + -1.6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + -1.6x + -0.6 + x2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + -1.6x + x2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + -1.6x + x2 = 0 + -0.6
-1.6x + x2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
-1.6x + x2 = -0.6

The x term is -1.6x.  Take half its coefficient (-0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
-1.6x + 0.64 + x2 = -0.6 + 0.64

Reorder the terms:
0.64 + -1.6x + x2 = -0.6 + 0.64

Combine like terms: -0.6 + 0.64 = 0.04
0.64 + -1.6x + x2 = 0.04

Factor a perfect square on the left side:
(x + -0.8)(x + -0.8) = 0.04

Calculate the square root of the right side: 0.2

Break this problem into two subproblems by setting 
(x + -0.8) equal to 0.2 and -0.2.

Subproblem 1
x + -0.8 = 0.2

Simplifying
x + -0.8 = 0.2

Reorder the terms:
-0.8 + x = 0.2

Solving
-0.8 + x = 0.2

Solving for variable 'x'.

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

Add '0.8' to each side of the equation.
-0.8 + 0.8 + x = 0.2 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + x = 0.2 + 0.8
x = 0.2 + 0.8

Combine like terms: 0.2 + 0.8 = 1
x = 1

Simplifying
x = 1

Subproblem 2
x + -0.8 = -0.2

Simplifying
x + -0.8 = -0.2

Reorder the terms:
-0.8 + x = -0.2

Solving
-0.8 + x = -0.2

Solving for variable 'x'.

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

Add '0.8' to each side of the equation.
-0.8 + 0.8 + x = -0.2 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + x = -0.2 + 0.8
x = -0.2 + 0.8

Combine like terms: -0.2 + 0.8 = 0.6
x = 0.6

Simplifying
x = 0.6

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1, 0.6}