x^2-4.8x+2.2=0

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Solution for x^2-4.8x+2.2=0 equation: 


Simplifying
x2 + -4.8x + 2.2 = 0

Reorder the terms:
2.2 + -4.8x + x2 = 0

Solving
2.2 + -4.8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2.2' to each side of the equation.
2.2 + -4.8x + -2.2 + x2 = 0 + -2.2

Reorder the terms:
2.2 + -2.2 + -4.8x + x2 = 0 + -2.2

Combine like terms: 2.2 + -2.2 = 0.0
0.0 + -4.8x + x2 = 0 + -2.2
-4.8x + x2 = 0 + -2.2

Combine like terms: 0 + -2.2 = -2.2
-4.8x + x2 = -2.2

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 = -2.2 + 5.76

Reorder the terms:
5.76 + -4.8x + x2 = -2.2 + 5.76

Combine like terms: -2.2 + 5.76 = 3.56
5.76 + -4.8x + x2 = 3.56

Factor a perfect square on the left side:
(x + -2.4)(x + -2.4) = 3.56

Calculate the square root of the right side: 1.886796226

Break this problem into two subproblems by setting 
(x + -2.4) equal to 1.886796226 and -1.886796226.


Subproblem 1
x + -2.4 = 1.886796226

Simplifying
x + -2.4 = 1.886796226

Reorder the terms:
-2.4 + x = 1.886796226

Solving
-2.4 + x = 1.886796226

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 = 1.886796226 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + x = 1.886796226 + 2.4
x = 1.886796226 + 2.4

Combine like terms: 1.886796226 + 2.4 = 4.286796226
x = 4.286796226

Simplifying
x = 4.286796226


Subproblem 2
x + -2.4 = -1.886796226

Simplifying
x + -2.4 = -1.886796226

Reorder the terms:
-2.4 + x = -1.886796226

Solving
-2.4 + x = -1.886796226

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 = -1.886796226 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + x = -1.886796226 + 2.4
x = -1.886796226 + 2.4

Combine like terms: -1.886796226 + 2.4 = 0.513203774
x = 0.513203774

Simplifying
x = 0.513203774


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.286796226, 0.513203774}

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