x^2-4.1x+2.1=0

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Solution for x^2-4.1x+2.1=0 equation: 


Simplifying
x2 + -4.1x + 2.1 = 0

Reorder the terms:
2.1 + -4.1x + x2 = 0

Solving
2.1 + -4.1x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2.1' to each side of the equation.
2.1 + -4.1x + -2.1 + x2 = 0 + -2.1

Reorder the terms:
2.1 + -2.1 + -4.1x + x2 = 0 + -2.1

Combine like terms: 2.1 + -2.1 = 0.0
0.0 + -4.1x + x2 = 0 + -2.1
-4.1x + x2 = 0 + -2.1

Combine like terms: 0 + -2.1 = -2.1
-4.1x + x2 = -2.1

The x term is -4.1x.  Take half its coefficient (-2.05).
Square it (4.2025) and add it to both sides.

Add '4.2025' to each side of the equation.
-4.1x + 4.2025 + x2 = -2.1 + 4.2025

Reorder the terms:
4.2025 + -4.1x + x2 = -2.1 + 4.2025

Combine like terms: -2.1 + 4.2025 = 2.1025
4.2025 + -4.1x + x2 = 2.1025

Factor a perfect square on the left side:
(x + -2.05)(x + -2.05) = 2.1025

Calculate the square root of the right side: 1.45

Break this problem into two subproblems by setting 
(x + -2.05) equal to 1.45 and -1.45.


Subproblem 1
x + -2.05 = 1.45

Simplifying
x + -2.05 = 1.45

Reorder the terms:
-2.05 + x = 1.45

Solving
-2.05 + x = 1.45

Solving for variable 'x'.

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

Add '2.05' to each side of the equation.
-2.05 + 2.05 + x = 1.45 + 2.05

Combine like terms: -2.05 + 2.05 = 0.00
0.00 + x = 1.45 + 2.05
x = 1.45 + 2.05

Combine like terms: 1.45 + 2.05 = 3.5
x = 3.5

Simplifying
x = 3.5


Subproblem 2
x + -2.05 = -1.45

Simplifying
x + -2.05 = -1.45

Reorder the terms:
-2.05 + x = -1.45

Solving
-2.05 + x = -1.45

Solving for variable 'x'.

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

Add '2.05' to each side of the equation.
-2.05 + 2.05 + x = -1.45 + 2.05

Combine like terms: -2.05 + 2.05 = 0.00
0.00 + x = -1.45 + 2.05
x = -1.45 + 2.05

Combine like terms: -1.45 + 2.05 = 0.6
x = 0.6

Simplifying
x = 0.6


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.5, 0.6}

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