x^2-4.2x+2=0

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


Simplifying
x2 + -4.2x + 2 = 0

Reorder the terms:
2 + -4.2x + x2 = 0

Solving
2 + -4.2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -4.2x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -4.2x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -4.2x + x2 = 0 + -2
-4.2x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-4.2x + x2 = -2

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 = -2 + 4.41

Reorder the terms:
4.41 + -4.2x + x2 = -2 + 4.41

Combine like terms: -2 + 4.41 = 2.41
4.41 + -4.2x + x2 = 2.41

Factor a perfect square on the left side:
(x + -2.1)(x + -2.1) = 2.41

Calculate the square root of the right side: 1.55241747

Break this problem into two subproblems by setting 
(x + -2.1) equal to 1.55241747 and -1.55241747.


Subproblem 1
x + -2.1 = 1.55241747

Simplifying
x + -2.1 = 1.55241747

Reorder the terms:
-2.1 + x = 1.55241747

Solving
-2.1 + x = 1.55241747

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 = 1.55241747 + 2.1

Combine like terms: -2.1 + 2.1 = 0.0
0.0 + x = 1.55241747 + 2.1
x = 1.55241747 + 2.1

Combine like terms: 1.55241747 + 2.1 = 3.65241747
x = 3.65241747

Simplifying
x = 3.65241747


Subproblem 2
x + -2.1 = -1.55241747

Simplifying
x + -2.1 = -1.55241747

Reorder the terms:
-2.1 + x = -1.55241747

Solving
-2.1 + x = -1.55241747

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 = -1.55241747 + 2.1

Combine like terms: -2.1 + 2.1 = 0.0
0.0 + x = -1.55241747 + 2.1
x = -1.55241747 + 2.1

Combine like terms: -1.55241747 + 2.1 = 0.54758253
x = 0.54758253

Simplifying
x = 0.54758253


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.65241747, 0.54758253}

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