x^2-4.2x+4.37=0

Solution for x^2-4.2x+4.37=0 equation:

Simplifying
x2 + -4.2x + 4.37 = 0

Reorder the terms:
4.37 + -4.2x + x2 = 0

Solving
4.37 + -4.2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-4.37' to each side of the equation.
4.37 + -4.2x + -4.37 + x2 = 0 + -4.37

Reorder the terms:
4.37 + -4.37 + -4.2x + x2 = 0 + -4.37

Combine like terms: 4.37 + -4.37 = 0.00
0.00 + -4.2x + x2 = 0 + -4.37
-4.2x + x2 = 0 + -4.37

Combine like terms: 0 + -4.37 = -4.37
-4.2x + x2 = -4.37

The x term is -4.2x.  Take half its coefficient (-2.1).
Square it (4.41) and add it to both sides.

Add '4.41' to each side of the equation.
-4.2x + 4.41 + x2 = -4.37 + 4.41

Reorder the terms:
4.41 + -4.2x + x2 = -4.37 + 4.41

Combine like terms: -4.37 + 4.41 = 0.04
4.41 + -4.2x + x2 = 0.04

Factor a perfect square on the left side:
(x + -2.1)(x + -2.1) = 0.04

Calculate the square root of the right side: 0.2

Break this problem into two subproblems by setting 
(x + -2.1) equal to 0.2 and -0.2.

Subproblem 1
x + -2.1 = 0.2

Simplifying
x + -2.1 = 0.2

Reorder the terms:
-2.1 + x = 0.2

Solving
-2.1 + x = 0.2

Solving for variable 'x'.

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

Add '2.1' to each side of the equation.
-2.1 + 2.1 + x = 0.2 + 2.1

Combine like terms: -2.1 + 2.1 = 0.0
0.0 + x = 0.2 + 2.1
x = 0.2 + 2.1

Combine like terms: 0.2 + 2.1 = 2.3
x = 2.3

Simplifying
x = 2.3

Subproblem 2
x + -2.1 = -0.2

Simplifying
x + -2.1 = -0.2

Reorder the terms:
-2.1 + x = -0.2

Solving
-2.1 + x = -0.2

Solving for variable 'x'.

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

Add '2.1' to each side of the equation.
-2.1 + 2.1 + x = -0.2 + 2.1

Combine like terms: -2.1 + 2.1 = 0.0
0.0 + x = -0.2 + 2.1
x = -0.2 + 2.1

Combine like terms: -0.2 + 2.1 = 1.9
x = 1.9

Simplifying
x = 1.9

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.3, 1.9}