0=x^2-5.6x+4.6

Solution for 0=x^2-5.6x+4.6 equation:

Simplifying
0 = x2 + -5.6x + 4.6

Reorder the terms:
0 = 4.6 + -5.6x + x2

Solving
0 = 4.6 + -5.6x + x2

Solving for variable 'x'.

Combine like terms: 0 + -4.6 = -4.6
-4.6 + 5.6x + -1x2 = 4.6 + -5.6x + x2 + -4.6 + 5.6x + -1x2

Reorder the terms:
-4.6 + 5.6x + -1x2 = 4.6 + -4.6 + -5.6x + 5.6x + x2 + -1x2

Combine like terms: 4.6 + -4.6 = 0.0
-4.6 + 5.6x + -1x2 = 0.0 + -5.6x + 5.6x + x2 + -1x2
-4.6 + 5.6x + -1x2 = -5.6x + 5.6x + x2 + -1x2

Combine like terms: -5.6x + 5.6x = 0.0
-4.6 + 5.6x + -1x2 = 0.0 + x2 + -1x2
-4.6 + 5.6x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-4.6 + 5.6x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
4.6 + -5.6x + x2 = 0

Move the constant term to the right:

Add '-4.6' to each side of the equation.
4.6 + -5.6x + -4.6 + x2 = 0 + -4.6

Reorder the terms:
4.6 + -4.6 + -5.6x + x2 = 0 + -4.6

Combine like terms: 4.6 + -4.6 = 0.0
0.0 + -5.6x + x2 = 0 + -4.6
-5.6x + x2 = 0 + -4.6

Combine like terms: 0 + -4.6 = -4.6
-5.6x + x2 = -4.6

The x term is -5.6x.  Take half its coefficient (-2.8).
Square it (7.84) and add it to both sides.

Add '7.84' to each side of the equation.
-5.6x + 7.84 + x2 = -4.6 + 7.84

Reorder the terms:
7.84 + -5.6x + x2 = -4.6 + 7.84

Combine like terms: -4.6 + 7.84 = 3.24
7.84 + -5.6x + x2 = 3.24

Factor a perfect square on the left side:
(x + -2.8)(x + -2.8) = 3.24

Calculate the square root of the right side: 1.8

Break this problem into two subproblems by setting 
(x + -2.8) equal to 1.8 and -1.8.

Subproblem 1
x + -2.8 = 1.8

Simplifying
x + -2.8 = 1.8

Reorder the terms:
-2.8 + x = 1.8

Solving
-2.8 + x = 1.8

Solving for variable 'x'.

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

Add '2.8' to each side of the equation.
-2.8 + 2.8 + x = 1.8 + 2.8

Combine like terms: -2.8 + 2.8 = 0.0
0.0 + x = 1.8 + 2.8
x = 1.8 + 2.8

Combine like terms: 1.8 + 2.8 = 4.6
x = 4.6

Simplifying
x = 4.6

Subproblem 2
x + -2.8 = -1.8

Simplifying
x + -2.8 = -1.8

Reorder the terms:
-2.8 + x = -1.8

Solving
-2.8 + x = -1.8

Solving for variable 'x'.

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

Add '2.8' to each side of the equation.
-2.8 + 2.8 + x = -1.8 + 2.8

Combine like terms: -2.8 + 2.8 = 0.0
0.0 + x = -1.8 + 2.8
x = -1.8 + 2.8

Combine like terms: -1.8 + 2.8 = 1
x = 1

Simplifying
x = 1

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.6, 1}