104.4x^2+33.3x-63=0

Solution for 104.4x^2+33.3x-63=0 equation:

Simplifying
104.4x2 + 33.3x + -63 = 0

Reorder the terms:
-63 + 33.3x + 104.4x2 = 0

Solving
-63 + 33.3x + 104.4x2 = 0

Solving for variable 'x'.

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

Divide each side by '104.4'.
-0.6034482759 + 0.3189655172x + x2 = 0

Move the constant term to the right:

Add '0.6034482759' to each side of the equation.
-0.6034482759 + 0.3189655172x + 0.6034482759 + x2 = 0 + 0.6034482759

Reorder the terms:
-0.6034482759 + 0.6034482759 + 0.3189655172x + x2 = 0 + 0.6034482759

Combine like terms: -0.6034482759 + 0.6034482759 = 0.0000000000
0.0000000000 + 0.3189655172x + x2 = 0 + 0.6034482759
0.3189655172x + x2 = 0 + 0.6034482759

Combine like terms: 0 + 0.6034482759 = 0.6034482759
0.3189655172x + x2 = 0.6034482759

The x term is 0.3189655172x.  Take half its coefficient (0.1594827586).
Square it (0.02543475029) and add it to both sides.

Add '0.02543475029' to each side of the equation.
0.3189655172x + 0.02543475029 + x2 = 0.6034482759 + 0.02543475029

Reorder the terms:
0.02543475029 + 0.3189655172x + x2 = 0.6034482759 + 0.02543475029

Combine like terms: 0.6034482759 + 0.02543475029 = 0.62888302619
0.02543475029 + 0.3189655172x + x2 = 0.62888302619

Factor a perfect square on the left side:
(x + 0.1594827586)(x + 0.1594827586) = 0.62888302619

Calculate the square root of the right side: 0.793021454

Break this problem into two subproblems by setting 
(x + 0.1594827586) equal to 0.793021454 and -0.793021454.

Subproblem 1
x + 0.1594827586 = 0.793021454

Simplifying
x + 0.1594827586 = 0.793021454

Reorder the terms:
0.1594827586 + x = 0.793021454

Solving
0.1594827586 + x = 0.793021454

Solving for variable 'x'.

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

Add '-0.1594827586' to each side of the equation.
0.1594827586 + -0.1594827586 + x = 0.793021454 + -0.1594827586

Combine like terms: 0.1594827586 + -0.1594827586 = 0.0000000000
0.0000000000 + x = 0.793021454 + -0.1594827586
x = 0.793021454 + -0.1594827586

Combine like terms: 0.793021454 + -0.1594827586 = 0.6335386954
x = 0.6335386954

Simplifying
x = 0.6335386954

Subproblem 2
x + 0.1594827586 = -0.793021454

Simplifying
x + 0.1594827586 = -0.793021454

Reorder the terms:
0.1594827586 + x = -0.793021454

Solving
0.1594827586 + x = -0.793021454

Solving for variable 'x'.

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

Add '-0.1594827586' to each side of the equation.
0.1594827586 + -0.1594827586 + x = -0.793021454 + -0.1594827586

Combine like terms: 0.1594827586 + -0.1594827586 = 0.0000000000
0.0000000000 + x = -0.793021454 + -0.1594827586
x = -0.793021454 + -0.1594827586

Combine like terms: -0.793021454 + -0.1594827586 = -0.9525042126
x = -0.9525042126

Simplifying
x = -0.9525042126

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.6335386954, -0.9525042126}