3.2x^2-16.8x+16.8=0

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Solution for 3.2x^2-16.8x+16.8=0 equation: 


Simplifying
3.2x2 + -16.8x + 16.8 = 0

Reorder the terms:
16.8 + -16.8x + 3.2x2 = 0

Solving
16.8 + -16.8x + 3.2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
3.2 the coefficient of the squared term: 

Divide each side by '3.2'.
5.25 + -5.25x + x2 = 0

Move the constant term to the right:

Add '-5.25' to each side of the equation.
5.25 + -5.25x + -5.25 + x2 = 0 + -5.25

Reorder the terms:
5.25 + -5.25 + -5.25x + x2 = 0 + -5.25

Combine like terms: 5.25 + -5.25 = 0.00
0.00 + -5.25x + x2 = 0 + -5.25
-5.25x + x2 = 0 + -5.25

Combine like terms: 0 + -5.25 = -5.25
-5.25x + x2 = -5.25

The x term is -5.25x.  Take half its coefficient (-2.625).
Square it (6.890625) and add it to both sides.

Add '6.890625' to each side of the equation.
-5.25x + 6.890625 + x2 = -5.25 + 6.890625

Reorder the terms:
6.890625 + -5.25x + x2 = -5.25 + 6.890625

Combine like terms: -5.25 + 6.890625 = 1.640625
6.890625 + -5.25x + x2 = 1.640625

Factor a perfect square on the left side:
(x + -2.625)(x + -2.625) = 1.640625

Calculate the square root of the right side: 1.280868846

Break this problem into two subproblems by setting 
(x + -2.625) equal to 1.280868846 and -1.280868846.


Subproblem 1
x + -2.625 = 1.280868846

Simplifying
x + -2.625 = 1.280868846

Reorder the terms:
-2.625 + x = 1.280868846

Solving
-2.625 + x = 1.280868846

Solving for variable 'x'.

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

Add '2.625' to each side of the equation.
-2.625 + 2.625 + x = 1.280868846 + 2.625

Combine like terms: -2.625 + 2.625 = 0.000
0.000 + x = 1.280868846 + 2.625
x = 1.280868846 + 2.625

Combine like terms: 1.280868846 + 2.625 = 3.905868846
x = 3.905868846

Simplifying
x = 3.905868846


Subproblem 2
x + -2.625 = -1.280868846

Simplifying
x + -2.625 = -1.280868846

Reorder the terms:
-2.625 + x = -1.280868846

Solving
-2.625 + x = -1.280868846

Solving for variable 'x'.

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

Add '2.625' to each side of the equation.
-2.625 + 2.625 + x = -1.280868846 + 2.625

Combine like terms: -2.625 + 2.625 = 0.000
0.000 + x = -1.280868846 + 2.625
x = -1.280868846 + 2.625

Combine like terms: -1.280868846 + 2.625 = 1.344131154
x = 1.344131154

Simplifying
x = 1.344131154


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.905868846, 1.344131154}

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