(0.4x^2)-34.4x=889.6

Solution for (0.4x^2)-34.4x=889.6 equation:

Simplifying
(0.4x2) + -34.4x = 889.6

Reorder the terms:
-34.4x + (0.4x2) = 889.6

Solving
-34.4x + (0.4x2) = 889.6

Solving for variable 'x'.

Reorder the terms:
-889.6 + -34.4x + (0.4x2) = 889.6 + -889.6

Combine like terms: 889.6 + -889.6 = 0.0
-889.6 + -34.4x + (0.4x2) = 0.0

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

Divide each side by '0.4'.
-2224 + -86x + x2 = 0

Move the constant term to the right:

Add '2224' to each side of the equation.
-2224 + -86x + 2224 + x2 = 0 + 2224

Reorder the terms:
-2224 + 2224 + -86x + x2 = 0 + 2224

Combine like terms: -2224 + 2224 = 0
0 + -86x + x2 = 0 + 2224
-86x + x2 = 0 + 2224

Combine like terms: 0 + 2224 = 2224
-86x + x2 = 2224

The x term is -86x.  Take half its coefficient (-43).
Square it (1849) and add it to both sides.

Add '1849' to each side of the equation.
-86x + 1849 + x2 = 2224 + 1849

Reorder the terms:
1849 + -86x + x2 = 2224 + 1849

Combine like terms: 2224 + 1849 = 4073
1849 + -86x + x2 = 4073

Factor a perfect square on the left side:
((x) + -43)((x) + -43) = 4073

Calculate the square root of the right side: 63.820059542

Break this problem into two subproblems by setting 
((x) + -43) equal to 63.820059542 and -63.820059542.

Subproblem 1
(x) + -43 = 63.820059542

Simplifying
(x) + -43 = 63.820059542
x + -43 = 63.820059542

Reorder the terms:
-43 + x = 63.820059542

Solving
-43 + x = 63.820059542

Solving for variable 'x'.

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

Add '43' to each side of the equation.
-43 + 43 + x = 63.820059542 + 43

Combine like terms: -43 + 43 = 0
0 + x = 63.820059542 + 43
x = 63.820059542 + 43

Combine like terms: 63.820059542 + 43 = 106.820059542
x = 106.820059542

Simplifying
x = 106.820059542

Subproblem 2
(x) + -43 = -63.820059542

Simplifying
(x) + -43 = -63.820059542
x + -43 = -63.820059542

Reorder the terms:
-43 + x = -63.820059542

Solving
-43 + x = -63.820059542

Solving for variable 'x'.

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

Add '43' to each side of the equation.
-43 + 43 + x = -63.820059542 + 43

Combine like terms: -43 + 43 = 0
0 + x = -63.820059542 + 43
x = -63.820059542 + 43

Combine like terms: -63.820059542 + 43 = -20.820059542
x = -20.820059542

Simplifying
x = -20.820059542

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {106.820059542, -20.820059542}