x*x-4.8x+2.1=0

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Solution for x*x-4.8x+2.1=0 equation: 


Simplifying
x * x + -4.8x + 2.1 = 0

Multiply x * x
x2 + -4.8x + 2.1 = 0

Reorder the terms:
2.1 + -4.8x + x2 = 0

Solving
2.1 + -4.8x + 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 + -4.8x + -2.1 + x2 = 0 + -2.1

Reorder the terms:
2.1 + -2.1 + -4.8x + x2 = 0 + -2.1

Combine like terms: 2.1 + -2.1 = 0.0
0.0 + -4.8x + x2 = 0 + -2.1
-4.8x + x2 = 0 + -2.1

Combine like terms: 0 + -2.1 = -2.1
-4.8x + x2 = -2.1

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 = -2.1 + 5.76

Reorder the terms:
5.76 + -4.8x + x2 = -2.1 + 5.76

Combine like terms: -2.1 + 5.76 = 3.66
5.76 + -4.8x + x2 = 3.66

Factor a perfect square on the left side:
(x + -2.4)(x + -2.4) = 3.66

Calculate the square root of the right side: 1.913112647

Break this problem into two subproblems by setting 
(x + -2.4) equal to 1.913112647 and -1.913112647.


Subproblem 1
x + -2.4 = 1.913112647

Simplifying
x + -2.4 = 1.913112647

Reorder the terms:
-2.4 + x = 1.913112647

Solving
-2.4 + x = 1.913112647

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 = 1.913112647 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + x = 1.913112647 + 2.4
x = 1.913112647 + 2.4

Combine like terms: 1.913112647 + 2.4 = 4.313112647
x = 4.313112647

Simplifying
x = 4.313112647


Subproblem 2
x + -2.4 = -1.913112647

Simplifying
x + -2.4 = -1.913112647

Reorder the terms:
-2.4 + x = -1.913112647

Solving
-2.4 + x = -1.913112647

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 = -1.913112647 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + x = -1.913112647 + 2.4
x = -1.913112647 + 2.4

Combine like terms: -1.913112647 + 2.4 = 0.486887353
x = 0.486887353

Simplifying
x = 0.486887353


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.313112647, 0.486887353}

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