x^2-5x+1.6=0

Solution for x^2-5x+1.6=0 equation:

Simplifying
x2 + -5x + 1.6 = 0

Reorder the terms:
1.6 + -5x + x2 = 0

Solving
1.6 + -5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-1.6' to each side of the equation.
1.6 + -5x + -1.6 + x2 = 0 + -1.6

Reorder the terms:
1.6 + -1.6 + -5x + x2 = 0 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + -5x + x2 = 0 + -1.6
-5x + x2 = 0 + -1.6

Combine like terms: 0 + -1.6 = -1.6
-5x + x2 = -1.6

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = -1.6 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -1.6 + 6.25

Combine like terms: -1.6 + 6.25 = 4.65
6.25 + -5x + x2 = 4.65

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 4.65

Calculate the square root of the right side: 2.156385865

Break this problem into two subproblems by setting 
(x + -2.5) equal to 2.156385865 and -2.156385865.

Subproblem 1
x + -2.5 = 2.156385865

Simplifying
x + -2.5 = 2.156385865

Reorder the terms:
-2.5 + x = 2.156385865

Solving
-2.5 + x = 2.156385865

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 2.156385865 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 2.156385865 + 2.5
x = 2.156385865 + 2.5

Combine like terms: 2.156385865 + 2.5 = 4.656385865
x = 4.656385865

Simplifying
x = 4.656385865

Subproblem 2
x + -2.5 = -2.156385865

Simplifying
x + -2.5 = -2.156385865

Reorder the terms:
-2.5 + x = -2.156385865

Solving
-2.5 + x = -2.156385865

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -2.156385865 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -2.156385865 + 2.5
x = -2.156385865 + 2.5

Combine like terms: -2.156385865 + 2.5 = 0.343614135
x = 0.343614135

Simplifying
x = 0.343614135

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.656385865, 0.343614135}