x^2-4.8x+2.3=0

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Solution for x^2-4.8x+2.3=0 equation: 


Simplifying
x2 + -4.8x + 2.3 = 0

Reorder the terms:
2.3 + -4.8x + x2 = 0

Solving
2.3 + -4.8x + 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 + -4.8x + -2.3 + x2 = 0 + -2.3

Reorder the terms:
2.3 + -2.3 + -4.8x + x2 = 0 + -2.3

Combine like terms: 2.3 + -2.3 = 0.0
0.0 + -4.8x + x2 = 0 + -2.3
-4.8x + x2 = 0 + -2.3

Combine like terms: 0 + -2.3 = -2.3
-4.8x + x2 = -2.3

The x term is -4.8x.  Take half its coefficient (-2.4).
Square it (5.76) and add it to both sides.

Add '5.76' to each side of the equation.
-4.8x + 5.76 + x2 = -2.3 + 5.76

Reorder the terms:
5.76 + -4.8x + x2 = -2.3 + 5.76

Combine like terms: -2.3 + 5.76 = 3.46
5.76 + -4.8x + x2 = 3.46

Factor a perfect square on the left side:
(x + -2.4)(x + -2.4) = 3.46

Calculate the square root of the right side: 1.860107524

Break this problem into two subproblems by setting 
(x + -2.4) equal to 1.860107524 and -1.860107524.


Subproblem 1
x + -2.4 = 1.860107524

Simplifying
x + -2.4 = 1.860107524

Reorder the terms:
-2.4 + x = 1.860107524

Solving
-2.4 + x = 1.860107524

Solving for variable 'x'.

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

Add '2.4' to each side of the equation.
-2.4 + 2.4 + x = 1.860107524 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + x = 1.860107524 + 2.4
x = 1.860107524 + 2.4

Combine like terms: 1.860107524 + 2.4 = 4.260107524
x = 4.260107524

Simplifying
x = 4.260107524


Subproblem 2
x + -2.4 = -1.860107524

Simplifying
x + -2.4 = -1.860107524

Reorder the terms:
-2.4 + x = -1.860107524

Solving
-2.4 + x = -1.860107524

Solving for variable 'x'.

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

Add '2.4' to each side of the equation.
-2.4 + 2.4 + x = -1.860107524 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + x = -1.860107524 + 2.4
x = -1.860107524 + 2.4

Combine like terms: -1.860107524 + 2.4 = 0.539892476
x = 0.539892476

Simplifying
x = 0.539892476


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.260107524, 0.539892476}

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