x^2-3x+.56=0

Solution for x^2-3x+.56=0 equation:

Simplifying
x2 + -3x + 0.56 = 0

Reorder the terms:
0.56 + -3x + x2 = 0

Solving
0.56 + -3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.56' to each side of the equation.
0.56 + -3x + -0.56 + x2 = 0 + -0.56

Reorder the terms:
0.56 + -0.56 + -3x + x2 = 0 + -0.56

Combine like terms: 0.56 + -0.56 = 0.00
0.00 + -3x + x2 = 0 + -0.56
-3x + x2 = 0 + -0.56

Combine like terms: 0 + -0.56 = -0.56
-3x + x2 = -0.56

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = -0.56 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -0.56 + 2.25

Combine like terms: -0.56 + 2.25 = 1.69
2.25 + -3x + x2 = 1.69

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 1.69

Calculate the square root of the right side: 1.3

Break this problem into two subproblems by setting 
(x + -1.5) equal to 1.3 and -1.3.

Subproblem 1
x + -1.5 = 1.3

Simplifying
x + -1.5 = 1.3

Reorder the terms:
-1.5 + x = 1.3

Solving
-1.5 + x = 1.3

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 1.3 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 1.3 + 1.5
x = 1.3 + 1.5

Combine like terms: 1.3 + 1.5 = 2.8
x = 2.8

Simplifying
x = 2.8

Subproblem 2
x + -1.5 = -1.3

Simplifying
x + -1.5 = -1.3

Reorder the terms:
-1.5 + x = -1.3

Solving
-1.5 + x = -1.3

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -1.3 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -1.3 + 1.5
x = -1.3 + 1.5

Combine like terms: -1.3 + 1.5 = 0.2
x = 0.2

Simplifying
x = 0.2

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.8, 0.2}