3.2x^2-12.6x+8.4=0

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Solution for 3.2x^2-12.6x+8.4=0 equation: 


Simplifying
3.2x2 + -12.6x + 8.4 = 0

Reorder the terms:
8.4 + -12.6x + 3.2x2 = 0

Solving
8.4 + -12.6x + 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'.
2.625 + -3.9375x + x2 = 0

Move the constant term to the right:

Add '-2.625' to each side of the equation.
2.625 + -3.9375x + -2.625 + x2 = 0 + -2.625

Reorder the terms:
2.625 + -2.625 + -3.9375x + x2 = 0 + -2.625

Combine like terms: 2.625 + -2.625 = 0.000
0.000 + -3.9375x + x2 = 0 + -2.625
-3.9375x + x2 = 0 + -2.625

Combine like terms: 0 + -2.625 = -2.625
-3.9375x + x2 = -2.625

The x term is -3.9375x.  Take half its coefficient (-1.96875).
Square it (3.875976563) and add it to both sides.

Add '3.875976563' to each side of the equation.
-3.9375x + 3.875976563 + x2 = -2.625 + 3.875976563

Reorder the terms:
3.875976563 + -3.9375x + x2 = -2.625 + 3.875976563

Combine like terms: -2.625 + 3.875976563 = 1.250976563
3.875976563 + -3.9375x + x2 = 1.250976563

Factor a perfect square on the left side:
(x + -1.96875)(x + -1.96875) = 1.250976563

Calculate the square root of the right side: 1.118470636

Break this problem into two subproblems by setting 
(x + -1.96875) equal to 1.118470636 and -1.118470636.


Subproblem 1
x + -1.96875 = 1.118470636

Simplifying
x + -1.96875 = 1.118470636

Reorder the terms:
-1.96875 + x = 1.118470636

Solving
-1.96875 + x = 1.118470636

Solving for variable 'x'.

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

Add '1.96875' to each side of the equation.
-1.96875 + 1.96875 + x = 1.118470636 + 1.96875

Combine like terms: -1.96875 + 1.96875 = 0.00000
0.00000 + x = 1.118470636 + 1.96875
x = 1.118470636 + 1.96875

Combine like terms: 1.118470636 + 1.96875 = 3.087220636
x = 3.087220636

Simplifying
x = 3.087220636


Subproblem 2
x + -1.96875 = -1.118470636

Simplifying
x + -1.96875 = -1.118470636

Reorder the terms:
-1.96875 + x = -1.118470636

Solving
-1.96875 + x = -1.118470636

Solving for variable 'x'.

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

Add '1.96875' to each side of the equation.
-1.96875 + 1.96875 + x = -1.118470636 + 1.96875

Combine like terms: -1.96875 + 1.96875 = 0.00000
0.00000 + x = -1.118470636 + 1.96875
x = -1.118470636 + 1.96875

Combine like terms: -1.118470636 + 1.96875 = 0.850279364
x = 0.850279364

Simplifying
x = 0.850279364


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.087220636, 0.850279364}

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