(x^2)-4.6x+2.8=0

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Solution for (x^2)-4.6x+2.8=0 equation: 


Simplifying
(x2) + -4.6x + 2.8 = 0
x2 + -4.6x + 2.8 = 0

Reorder the terms:
2.8 + -4.6x + x2 = 0

Solving
2.8 + -4.6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2.8' to each side of the equation.
2.8 + -4.6x + -2.8 + x2 = 0 + -2.8

Reorder the terms:
2.8 + -2.8 + -4.6x + x2 = 0 + -2.8

Combine like terms: 2.8 + -2.8 = 0.0
0.0 + -4.6x + x2 = 0 + -2.8
-4.6x + x2 = 0 + -2.8

Combine like terms: 0 + -2.8 = -2.8
-4.6x + x2 = -2.8

The x term is -4.6x.  Take half its coefficient (-2.3).
Square it (5.29) and add it to both sides.

Add '5.29' to each side of the equation.
-4.6x + 5.29 + x2 = -2.8 + 5.29

Reorder the terms:
5.29 + -4.6x + x2 = -2.8 + 5.29

Combine like terms: -2.8 + 5.29 = 2.49
5.29 + -4.6x + x2 = 2.49

Factor a perfect square on the left side:
(x + -2.3)(x + -2.3) = 2.49

Calculate the square root of the right side: 1.577973384

Break this problem into two subproblems by setting 
(x + -2.3) equal to 1.577973384 and -1.577973384.


Subproblem 1
x + -2.3 = 1.577973384

Simplifying
x + -2.3 = 1.577973384

Reorder the terms:
-2.3 + x = 1.577973384

Solving
-2.3 + x = 1.577973384

Solving for variable 'x'.

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

Add '2.3' to each side of the equation.
-2.3 + 2.3 + x = 1.577973384 + 2.3

Combine like terms: -2.3 + 2.3 = 0.0
0.0 + x = 1.577973384 + 2.3
x = 1.577973384 + 2.3

Combine like terms: 1.577973384 + 2.3 = 3.877973384
x = 3.877973384

Simplifying
x = 3.877973384


Subproblem 2
x + -2.3 = -1.577973384

Simplifying
x + -2.3 = -1.577973384

Reorder the terms:
-2.3 + x = -1.577973384

Solving
-2.3 + x = -1.577973384

Solving for variable 'x'.

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

Add '2.3' to each side of the equation.
-2.3 + 2.3 + x = -1.577973384 + 2.3

Combine like terms: -2.3 + 2.3 = 0.0
0.0 + x = -1.577973384 + 2.3
x = -1.577973384 + 2.3

Combine like terms: -1.577973384 + 2.3 = 0.722026616
x = 0.722026616

Simplifying
x = 0.722026616


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.877973384, 0.722026616}

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