.5*(447.9)*3.8*(x+1.27)+10.4x^2-298.1x^2=0

Solution for .5*(447.9)*3.8*(x+1.27)+10.4x^2-298.1x^2=0 equation:

Simplifying
0.5(447.9) * 3.8(x + 1.27) + 10.4x2 + -298.1x2 = 0

Reorder the terms:
0.5 * 447.9 * 3.8(1.27 + x) + 10.4x2 + -298.1x2 = 0

Multiply 0.5 * 447.9
223.95 * 3.8(1.27 + x) + 10.4x2 + -298.1x2 = 0

Multiply 223.95 * 3.8
851.01(1.27 + x) + 10.4x2 + -298.1x2 = 0
(1.27 * 851.01 + x * 851.01) + 10.4x2 + -298.1x2 = 0
(1080.7827 + 851.01x) + 10.4x2 + -298.1x2 = 0

Combine like terms: 10.4x2 + -298.1x2 = -287.7x2
1080.7827 + 851.01x + -287.7x2 = 0

Solving
1080.7827 + 851.01x + -287.7x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-287.7 the coefficient of the squared term: 

Divide each side by '-287.7'.
-3.756630865 + -2.957977059x + x2 = 0

Move the constant term to the right:

Add '3.756630865' to each side of the equation.
-3.756630865 + -2.957977059x + 3.756630865 + x2 = 0 + 3.756630865

Reorder the terms:
-3.756630865 + 3.756630865 + -2.957977059x + x2 = 0 + 3.756630865

Combine like terms: -3.756630865 + 3.756630865 = 0.000000000
0.000000000 + -2.957977059x + x2 = 0 + 3.756630865
-2.957977059x + x2 = 0 + 3.756630865

Combine like terms: 0 + 3.756630865 = 3.756630865
-2.957977059x + x2 = 3.756630865

The x term is -2.957977059x.  Take half its coefficient (-1.47898853).
Square it (2.187407072) and add it to both sides.

Add '2.187407072' to each side of the equation.
-2.957977059x + 2.187407072 + x2 = 3.756630865 + 2.187407072

Reorder the terms:
2.187407072 + -2.957977059x + x2 = 3.756630865 + 2.187407072

Combine like terms: 3.756630865 + 2.187407072 = 5.944037937
2.187407072 + -2.957977059x + x2 = 5.944037937

Factor a perfect square on the left side:
(x + -1.47898853)(x + -1.47898853) = 5.944037937

Calculate the square root of the right side: 2.438039773

Break this problem into two subproblems by setting 
(x + -1.47898853) equal to 2.438039773 and -2.438039773.

Subproblem 1
x + -1.47898853 = 2.438039773

Simplifying
x + -1.47898853 = 2.438039773

Reorder the terms:
-1.47898853 + x = 2.438039773

Solving
-1.47898853 + x = 2.438039773

Solving for variable 'x'.

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

Add '1.47898853' to each side of the equation.
-1.47898853 + 1.47898853 + x = 2.438039773 + 1.47898853

Combine like terms: -1.47898853 + 1.47898853 = 0.00000000
0.00000000 + x = 2.438039773 + 1.47898853
x = 2.438039773 + 1.47898853

Combine like terms: 2.438039773 + 1.47898853 = 3.917028303
x = 3.917028303

Simplifying
x = 3.917028303

Subproblem 2
x + -1.47898853 = -2.438039773

Simplifying
x + -1.47898853 = -2.438039773

Reorder the terms:
-1.47898853 + x = -2.438039773

Solving
-1.47898853 + x = -2.438039773

Solving for variable 'x'.

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

Add '1.47898853' to each side of the equation.
-1.47898853 + 1.47898853 + x = -2.438039773 + 1.47898853

Combine like terms: -1.47898853 + 1.47898853 = 0.00000000
0.00000000 + x = -2.438039773 + 1.47898853
x = -2.438039773 + 1.47898853

Combine like terms: -2.438039773 + 1.47898853 = -0.959051243
x = -0.959051243

Simplifying
x = -0.959051243

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.917028303, -0.959051243}