x^2-1.6x+0.15=0

Solution for x^2-1.6x+0.15=0 equation:

Simplifying
x2 + -1.6x + 0.15 = 0

Reorder the terms:
0.15 + -1.6x + x2 = 0

Solving
0.15 + -1.6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.15' to each side of the equation.
0.15 + -1.6x + -0.15 + x2 = 0 + -0.15

Reorder the terms:
0.15 + -0.15 + -1.6x + x2 = 0 + -0.15

Combine like terms: 0.15 + -0.15 = 0.00
0.00 + -1.6x + x2 = 0 + -0.15
-1.6x + x2 = 0 + -0.15

Combine like terms: 0 + -0.15 = -0.15
-1.6x + x2 = -0.15

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 = -0.15 + 0.64

Reorder the terms:
0.64 + -1.6x + x2 = -0.15 + 0.64

Combine like terms: -0.15 + 0.64 = 0.49
0.64 + -1.6x + x2 = 0.49

Factor a perfect square on the left side:
(x + -0.8)(x + -0.8) = 0.49

Calculate the square root of the right side: 0.7

Break this problem into two subproblems by setting 
(x + -0.8) equal to 0.7 and -0.7.

Subproblem 1
x + -0.8 = 0.7

Simplifying
x + -0.8 = 0.7

Reorder the terms:
-0.8 + x = 0.7

Solving
-0.8 + x = 0.7

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 = 0.7 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + x = 0.7 + 0.8
x = 0.7 + 0.8

Combine like terms: 0.7 + 0.8 = 1.5
x = 1.5

Simplifying
x = 1.5

Subproblem 2
x + -0.8 = -0.7

Simplifying
x + -0.8 = -0.7

Reorder the terms:
-0.8 + x = -0.7

Solving
-0.8 + x = -0.7

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 = -0.7 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + x = -0.7 + 0.8
x = -0.7 + 0.8

Combine like terms: -0.7 + 0.8 = 0.1
x = 0.1

Simplifying
x = 0.1

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.5, 0.1}