x^2-3.2x-6.44=0

Solution for x^2-3.2x-6.44=0 equation:

Simplifying
x2 + -3.2x + -6.44 = 0

Reorder the terms:
-6.44 + -3.2x + x2 = 0

Solving
-6.44 + -3.2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '6.44' to each side of the equation.
-6.44 + -3.2x + 6.44 + x2 = 0 + 6.44

Reorder the terms:
-6.44 + 6.44 + -3.2x + x2 = 0 + 6.44

Combine like terms: -6.44 + 6.44 = 0.00
0.00 + -3.2x + x2 = 0 + 6.44
-3.2x + x2 = 0 + 6.44

Combine like terms: 0 + 6.44 = 6.44
-3.2x + x2 = 6.44

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 = 6.44 + 2.56

Reorder the terms:
2.56 + -3.2x + x2 = 6.44 + 2.56

Combine like terms: 6.44 + 2.56 = 9
2.56 + -3.2x + x2 = 9

Factor a perfect square on the left side:
(x + -1.6)(x + -1.6) = 9

Calculate the square root of the right side: 3

Break this problem into two subproblems by setting 
(x + -1.6) equal to 3 and -3.

Subproblem 1
x + -1.6 = 3

Simplifying
x + -1.6 = 3

Reorder the terms:
-1.6 + x = 3

Solving
-1.6 + x = 3

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 = 3 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + x = 3 + 1.6
x = 3 + 1.6

Combine like terms: 3 + 1.6 = 4.6
x = 4.6

Simplifying
x = 4.6

Subproblem 2
x + -1.6 = -3

Simplifying
x + -1.6 = -3

Reorder the terms:
-1.6 + x = -3

Solving
-1.6 + x = -3

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 = -3 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + x = -3 + 1.6
x = -3 + 1.6

Combine like terms: -3 + 1.6 = -1.4
x = -1.4

Simplifying
x = -1.4

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.6, -1.4}