x=.0002x^2-.316(750)+127.9

Solution for x=.0002x^2-.316(750)+127.9 equation:

Simplifying
x = 0.0002x2 + -0.316(750) + 127.9

Multiply -0.316 * 750
x = 0.0002x2 + -237 + 127.9

Reorder the terms:
x = -237 + 127.9 + 0.0002x2

Combine like terms: -237 + 127.9 = -109.1
x = -109.1 + 0.0002x2

Solving
x = -109.1 + 0.0002x2

Solving for variable 'x'.

Reorder the terms:
109.1 + x + -0.0002x2 = -109.1 + 0.0002x2 + 109.1 + -0.0002x2

Reorder the terms:
109.1 + x + -0.0002x2 = -109.1 + 109.1 + 0.0002x2 + -0.0002x2

Combine like terms: -109.1 + 109.1 = 0.0
109.1 + x + -0.0002x2 = 0.0 + 0.0002x2 + -0.0002x2
109.1 + x + -0.0002x2 = 0.0002x2 + -0.0002x2

Combine like terms: 0.0002x2 + -0.0002x2 = 0.0000
109.1 + x + -0.0002x2 = 0.0000

Begin completing the square.  Divide all terms by
-0.0002 the coefficient of the squared term: 

Divide each side by '-0.0002'.
-545500 + -5000x + x2 = 0

Move the constant term to the right:

Add '545500' to each side of the equation.
-545500 + -5000x + 545500 + x2 = 0 + 545500

Reorder the terms:
-545500 + 545500 + -5000x + x2 = 0 + 545500

Combine like terms: -545500 + 545500 = 0
0 + -5000x + x2 = 0 + 545500
-5000x + x2 = 0 + 545500

Combine like terms: 0 + 545500 = 545500
-5000x + x2 = 545500

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-5000x + 0.25 + x2 = 545500 + 0.25

Reorder the terms:
0.25 + -5000x + x2 = 545500 + 0.25

Combine like terms: 545500 + 0.25 = 545500.25
0.25 + -5000x + x2 = 545500.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 545500.25

Calculate the square root of the right side: 738.579887351

Break this problem into two subproblems by setting 
(x + 0.5) equal to 738.579887351 and -738.579887351.

Subproblem 1
x + 0.5 = 738.579887351

Simplifying
x + 0.5 = 738.579887351

Reorder the terms:
0.5 + x = 738.579887351

Solving
0.5 + x = 738.579887351

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 738.579887351 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 738.579887351 + -0.5
x = 738.579887351 + -0.5

Combine like terms: 738.579887351 + -0.5 = 738.079887351
x = 738.079887351

Simplifying
x = 738.079887351

Subproblem 2
x + 0.5 = -738.579887351

Simplifying
x + 0.5 = -738.579887351

Reorder the terms:
0.5 + x = -738.579887351

Solving
0.5 + x = -738.579887351

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -738.579887351 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -738.579887351 + -0.5
x = -738.579887351 + -0.5

Combine like terms: -738.579887351 + -0.5 = -739.079887351
x = -739.079887351

Simplifying
x = -739.079887351

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {738.079887351, -739.079887351}