4=.0002x^2-.316x+127.9

Solution for 4=.0002x^2-.316x+127.9 equation:

Simplifying
4 = 0.0002x2 + -0.316x + 127.9

Reorder the terms:
4 = 127.9 + -0.316x + 0.0002x2

Solving
4 = 127.9 + -0.316x + 0.0002x2

Solving for variable 'x'.

Combine like terms: 4 + -127.9 = -123.9
-123.9 + 0.316x + -0.0002x2 = 127.9 + -0.316x + 0.0002x2 + -127.9 + 0.316x + -0.0002x2

Reorder the terms:
-123.9 + 0.316x + -0.0002x2 = 127.9 + -127.9 + -0.316x + 0.316x + 0.0002x2 + -0.0002x2

Combine like terms: 127.9 + -127.9 = 0.0
-123.9 + 0.316x + -0.0002x2 = 0.0 + -0.316x + 0.316x + 0.0002x2 + -0.0002x2
-123.9 + 0.316x + -0.0002x2 = -0.316x + 0.316x + 0.0002x2 + -0.0002x2

Combine like terms: -0.316x + 0.316x = 0.000
-123.9 + 0.316x + -0.0002x2 = 0.000 + 0.0002x2 + -0.0002x2
-123.9 + 0.316x + -0.0002x2 = 0.0002x2 + -0.0002x2

Combine like terms: 0.0002x2 + -0.0002x2 = 0.0000
-123.9 + 0.316x + -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'.
619500 + -1580x + x2 = 0

Move the constant term to the right:

Add '-619500' to each side of the equation.
619500 + -1580x + -619500 + x2 = 0 + -619500

Reorder the terms:
619500 + -619500 + -1580x + x2 = 0 + -619500

Combine like terms: 619500 + -619500 = 0
0 + -1580x + x2 = 0 + -619500
-1580x + x2 = 0 + -619500

Combine like terms: 0 + -619500 = -619500
-1580x + x2 = -619500

The x term is -1580x.  Take half its coefficient (-790).
Square it (624100) and add it to both sides.

Add '624100' to each side of the equation.
-1580x + 624100 + x2 = -619500 + 624100

Reorder the terms:
624100 + -1580x + x2 = -619500 + 624100

Combine like terms: -619500 + 624100 = 4600
624100 + -1580x + x2 = 4600

Factor a perfect square on the left side:
(x + -790)(x + -790) = 4600

Calculate the square root of the right side: 67.823299831

Break this problem into two subproblems by setting 
(x + -790) equal to 67.823299831 and -67.823299831.

Subproblem 1
x + -790 = 67.823299831

Simplifying
x + -790 = 67.823299831

Reorder the terms:
-790 + x = 67.823299831

Solving
-790 + x = 67.823299831

Solving for variable 'x'.

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

Add '790' to each side of the equation.
-790 + 790 + x = 67.823299831 + 790

Combine like terms: -790 + 790 = 0
0 + x = 67.823299831 + 790
x = 67.823299831 + 790

Combine like terms: 67.823299831 + 790 = 857.823299831
x = 857.823299831

Simplifying
x = 857.823299831

Subproblem 2
x + -790 = -67.823299831

Simplifying
x + -790 = -67.823299831

Reorder the terms:
-790 + x = -67.823299831

Solving
-790 + x = -67.823299831

Solving for variable 'x'.

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

Add '790' to each side of the equation.
-790 + 790 + x = -67.823299831 + 790

Combine like terms: -790 + 790 = 0
0 + x = -67.823299831 + 790
x = -67.823299831 + 790

Combine like terms: -67.823299831 + 790 = 722.176700169
x = 722.176700169

Simplifying
x = 722.176700169

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {857.823299831, 722.176700169}