x*x-4.2x+2.8=0

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Solution for x*x-4.2x+2.8=0 equation: 


Simplifying
x * x + -4.2x + 2.8 = 0

Multiply x * x
x2 + -4.2x + 2.8 = 0

Reorder the terms:
2.8 + -4.2x + x2 = 0

Solving
2.8 + -4.2x + 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 + -4.2x + -2.8 + x2 = 0 + -2.8

Reorder the terms:
2.8 + -2.8 + -4.2x + x2 = 0 + -2.8

Combine like terms: 2.8 + -2.8 = 0.0
0.0 + -4.2x + x2 = 0 + -2.8
-4.2x + x2 = 0 + -2.8

Combine like terms: 0 + -2.8 = -2.8
-4.2x + x2 = -2.8

The x term is -4.2x.  Take half its coefficient (-2.1).
Square it (4.41) and add it to both sides.

Add '4.41' to each side of the equation.
-4.2x + 4.41 + x2 = -2.8 + 4.41

Reorder the terms:
4.41 + -4.2x + x2 = -2.8 + 4.41

Combine like terms: -2.8 + 4.41 = 1.61
4.41 + -4.2x + x2 = 1.61

Factor a perfect square on the left side:
(x + -2.1)(x + -2.1) = 1.61

Calculate the square root of the right side: 1.268857754

Break this problem into two subproblems by setting 
(x + -2.1) equal to 1.268857754 and -1.268857754.


Subproblem 1
x + -2.1 = 1.268857754

Simplifying
x + -2.1 = 1.268857754

Reorder the terms:
-2.1 + x = 1.268857754

Solving
-2.1 + x = 1.268857754

Solving for variable 'x'.

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

Add '2.1' to each side of the equation.
-2.1 + 2.1 + x = 1.268857754 + 2.1

Combine like terms: -2.1 + 2.1 = 0.0
0.0 + x = 1.268857754 + 2.1
x = 1.268857754 + 2.1

Combine like terms: 1.268857754 + 2.1 = 3.368857754
x = 3.368857754

Simplifying
x = 3.368857754


Subproblem 2
x + -2.1 = -1.268857754

Simplifying
x + -2.1 = -1.268857754

Reorder the terms:
-2.1 + x = -1.268857754

Solving
-2.1 + x = -1.268857754

Solving for variable 'x'.

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

Add '2.1' to each side of the equation.
-2.1 + 2.1 + x = -1.268857754 + 2.1

Combine like terms: -2.1 + 2.1 = 0.0
0.0 + x = -1.268857754 + 2.1
x = -1.268857754 + 2.1

Combine like terms: -1.268857754 + 2.1 = 0.831142246
x = 0.831142246

Simplifying
x = 0.831142246


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.368857754, 0.831142246}

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