.0002x^2-.316x+127.9=9

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Solution for .0002x^2-.316x+127.9=9 equation: 


Simplifying
0.0002x2 + -0.316x + 127.9 = 9

Reorder the terms:
127.9 + -0.316x + 0.0002x2 = 9

Solving
127.9 + -0.316x + 0.0002x2 = 9

Solving for variable 'x'.

Reorder the terms:
127.9 + -9 + -0.316x + 0.0002x2 = 9 + -9

Combine like terms: 127.9 + -9 = 118.9
118.9 + -0.316x + 0.0002x2 = 9 + -9

Combine like terms: 9 + -9 = 0
118.9 + -0.316x + 0.0002x2 = 0

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

Divide each side by '0.0002'.
594500 + -1580x + x2 = 0

Move the constant term to the right:

Add '-594500' to each side of the equation.
594500 + -1580x + -594500 + x2 = 0 + -594500

Reorder the terms:
594500 + -594500 + -1580x + x2 = 0 + -594500

Combine like terms: 594500 + -594500 = 0
0 + -1580x + x2 = 0 + -594500
-1580x + x2 = 0 + -594500

Combine like terms: 0 + -594500 = -594500
-1580x + x2 = -594500

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 = -594500 + 624100

Reorder the terms:
624100 + -1580x + x2 = -594500 + 624100

Combine like terms: -594500 + 624100 = 29600
624100 + -1580x + x2 = 29600

Factor a perfect square on the left side:
(x + -790)(x + -790) = 29600

Calculate the square root of the right side: 172.046505341

Break this problem into two subproblems by setting 
(x + -790) equal to 172.046505341 and -172.046505341.


Subproblem 1
x + -790 = 172.046505341

Simplifying
x + -790 = 172.046505341

Reorder the terms:
-790 + x = 172.046505341

Solving
-790 + x = 172.046505341

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 = 172.046505341 + 790

Combine like terms: -790 + 790 = 0
0 + x = 172.046505341 + 790
x = 172.046505341 + 790

Combine like terms: 172.046505341 + 790 = 962.046505341
x = 962.046505341

Simplifying
x = 962.046505341


Subproblem 2
x + -790 = -172.046505341

Simplifying
x + -790 = -172.046505341

Reorder the terms:
-790 + x = -172.046505341

Solving
-790 + x = -172.046505341

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 = -172.046505341 + 790

Combine like terms: -790 + 790 = 0
0 + x = -172.046505341 + 790
x = -172.046505341 + 790

Combine like terms: -172.046505341 + 790 = 617.953494659
x = 617.953494659

Simplifying
x = 617.953494659


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {962.046505341, 617.953494659}

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