x^2-3.2x+1.35=0

Solution for x^2-3.2x+1.35=0 equation:

Simplifying
x2 + -3.2x + 1.35 = 0

Reorder the terms:
1.35 + -3.2x + x2 = 0

Solving
1.35 + -3.2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-1.35' to each side of the equation.
1.35 + -3.2x + -1.35 + x2 = 0 + -1.35

Reorder the terms:
1.35 + -1.35 + -3.2x + x2 = 0 + -1.35

Combine like terms: 1.35 + -1.35 = 0.00
0.00 + -3.2x + x2 = 0 + -1.35
-3.2x + x2 = 0 + -1.35

Combine like terms: 0 + -1.35 = -1.35
-3.2x + x2 = -1.35

The x term is -3.2x.  Take half its coefficient (-1.6).
Square it (2.56) and add it to both sides.

Add '2.56' to each side of the equation.
-3.2x + 2.56 + x2 = -1.35 + 2.56

Reorder the terms:
2.56 + -3.2x + x2 = -1.35 + 2.56

Combine like terms: -1.35 + 2.56 = 1.21
2.56 + -3.2x + x2 = 1.21

Factor a perfect square on the left side:
(x + -1.6)(x + -1.6) = 1.21

Calculate the square root of the right side: 1.1

Break this problem into two subproblems by setting 
(x + -1.6) equal to 1.1 and -1.1.

Subproblem 1
x + -1.6 = 1.1

Simplifying
x + -1.6 = 1.1

Reorder the terms:
-1.6 + x = 1.1

Solving
-1.6 + x = 1.1

Solving for variable 'x'.

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

Add '1.6' to each side of the equation.
-1.6 + 1.6 + x = 1.1 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + x = 1.1 + 1.6
x = 1.1 + 1.6

Combine like terms: 1.1 + 1.6 = 2.7
x = 2.7

Simplifying
x = 2.7

Subproblem 2
x + -1.6 = -1.1

Simplifying
x + -1.6 = -1.1

Reorder the terms:
-1.6 + x = -1.1

Solving
-1.6 + x = -1.1

Solving for variable 'x'.

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

Add '1.6' to each side of the equation.
-1.6 + 1.6 + x = -1.1 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + x = -1.1 + 1.6
x = -1.1 + 1.6

Combine like terms: -1.1 + 1.6 = 0.5
x = 0.5

Simplifying
x = 0.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.7, 0.5}