1=314.011706*x+24672.00111525761*x^2

Solution for 1=314.011706*x+24672.00111525761*x^2 equation:

Simplifying
1 = 314.011706x + 24672.00111525761x2

Solving
1 = 314.011706x + 24672.00111525761x2

Solving for variable 'x'.

Reorder the terms:
1 + -314.011706x + -24672.00111525761x2 = 314.011706x + -314.011706x + 24672.00111525761x2 + -24672.00111525761x2

Combine like terms: 314.011706x + -314.011706x = 0.000000
1 + -314.011706x + -24672.00111525761x2 = 0.000000 + 24672.00111525761x2 + -24672.00111525761x2
1 + -314.011706x + -24672.00111525761x2 = 24672.00111525761x2 + -24672.00111525761x2

Combine like terms: 24672.00111525761x2 + -24672.00111525761x2 = 0.00000000000
1 + -314.011706x + -24672.00111525761x2 = 0.00000000000

Begin completing the square.  Divide all terms by
-24672.00111525761 the coefficient of the squared term: 

Divide each side by '-24672.00111525761'.
-0.00004053177508 + 0.01272745184x + x2 = 0

Move the constant term to the right:

Add '0.00004053177508' to each side of the equation.
-0.00004053177508 + 0.01272745184x + 0.00004053177508 + x2 = 0 + 0.00004053177508

Reorder the terms:
-0.00004053177508 + 0.00004053177508 + 0.01272745184x + x2 = 0 + 0.00004053177508

Combine like terms: -0.00004053177508 + 0.00004053177508 = 0.00000000000000
0.00000000000000 + 0.01272745184x + x2 = 0 + 0.00004053177508
0.01272745184x + x2 = 0 + 0.00004053177508

Combine like terms: 0 + 0.00004053177508 = 0.00004053177508
0.01272745184x + x2 = 0.00004053177508

The x term is 0.01272745184x.  Take half its coefficient (0.00636372592).
Square it (0.00004049700758) and add it to both sides.

Add '0.00004049700758' to each side of the equation.
0.01272745184x + 0.00004049700758 + x2 = 0.00004053177508 + 0.00004049700758

Reorder the terms:
0.00004049700758 + 0.01272745184x + x2 = 0.00004053177508 + 0.00004049700758

Combine like terms: 0.00004053177508 + 0.00004049700758 = 0.00008102878266
0.00004049700758 + 0.01272745184x + x2 = 0.00008102878266

Factor a perfect square on the left side:
(x + 0.00636372592)(x + 0.00636372592) = 0.00008102878266

Calculate the square root of the right side: 0.009001599

Break this problem into two subproblems by setting 
(x + 0.00636372592) equal to 0.009001599 and -0.009001599.

Subproblem 1
x + 0.00636372592 = 0.009001599

Simplifying
x + 0.00636372592 = 0.009001599

Reorder the terms:
0.00636372592 + x = 0.009001599

Solving
0.00636372592 + x = 0.009001599

Solving for variable 'x'.

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

Add '-0.00636372592' to each side of the equation.
0.00636372592 + -0.00636372592 + x = 0.009001599 + -0.00636372592

Combine like terms: 0.00636372592 + -0.00636372592 = 0.00000000000
0.00000000000 + x = 0.009001599 + -0.00636372592
x = 0.009001599 + -0.00636372592

Combine like terms: 0.009001599 + -0.00636372592 = 0.00263787308
x = 0.00263787308

Simplifying
x = 0.00263787308

Subproblem 2
x + 0.00636372592 = -0.009001599

Simplifying
x + 0.00636372592 = -0.009001599

Reorder the terms:
0.00636372592 + x = -0.009001599

Solving
0.00636372592 + x = -0.009001599

Solving for variable 'x'.

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

Add '-0.00636372592' to each side of the equation.
0.00636372592 + -0.00636372592 + x = -0.009001599 + -0.00636372592

Combine like terms: 0.00636372592 + -0.00636372592 = 0.00000000000
0.00000000000 + x = -0.009001599 + -0.00636372592
x = -0.009001599 + -0.00636372592

Combine like terms: -0.009001599 + -0.00636372592 = -0.01536532492
x = -0.01536532492

Simplifying
x = -0.01536532492

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.00263787308, -0.01536532492}