x^2-4.1x+2.3=0

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Solution for x^2-4.1x+2.3=0 equation: 


Simplifying
x2 + -4.1x + 2.3 = 0

Reorder the terms:
2.3 + -4.1x + x2 = 0

Solving
2.3 + -4.1x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2.3' to each side of the equation.
2.3 + -4.1x + -2.3 + x2 = 0 + -2.3

Reorder the terms:
2.3 + -2.3 + -4.1x + x2 = 0 + -2.3

Combine like terms: 2.3 + -2.3 = 0.0
0.0 + -4.1x + x2 = 0 + -2.3
-4.1x + x2 = 0 + -2.3

Combine like terms: 0 + -2.3 = -2.3
-4.1x + x2 = -2.3

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 = -2.3 + 4.2025

Reorder the terms:
4.2025 + -4.1x + x2 = -2.3 + 4.2025

Combine like terms: -2.3 + 4.2025 = 1.9025
4.2025 + -4.1x + x2 = 1.9025

Factor a perfect square on the left side:
(x + -2.05)(x + -2.05) = 1.9025

Calculate the square root of the right side: 1.379311422

Break this problem into two subproblems by setting 
(x + -2.05) equal to 1.379311422 and -1.379311422.


Subproblem 1
x + -2.05 = 1.379311422

Simplifying
x + -2.05 = 1.379311422

Reorder the terms:
-2.05 + x = 1.379311422

Solving
-2.05 + x = 1.379311422

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 = 1.379311422 + 2.05

Combine like terms: -2.05 + 2.05 = 0.00
0.00 + x = 1.379311422 + 2.05
x = 1.379311422 + 2.05

Combine like terms: 1.379311422 + 2.05 = 3.429311422
x = 3.429311422

Simplifying
x = 3.429311422


Subproblem 2
x + -2.05 = -1.379311422

Simplifying
x + -2.05 = -1.379311422

Reorder the terms:
-2.05 + x = -1.379311422

Solving
-2.05 + x = -1.379311422

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 = -1.379311422 + 2.05

Combine like terms: -2.05 + 2.05 = 0.00
0.00 + x = -1.379311422 + 2.05
x = -1.379311422 + 2.05

Combine like terms: -1.379311422 + 2.05 = 0.670688578
x = 0.670688578

Simplifying
x = 0.670688578


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.429311422, 0.670688578}

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