-1x^2+24673.20799626468x+314.019418=0

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Solution for -1x^2+24673.20799626468x+314.019418=0 equation: 


Simplifying
-1x2 + 24673.20799626468x + 314.019418 = 0

Reorder the terms:
314.019418 + 24673.20799626468x + -1x2 = 0

Solving
314.019418 + 24673.20799626468x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-314.019418 + -24673.208x + x2 = 0

Move the constant term to the right:

Add '314.019418' to each side of the equation.
-314.019418 + -24673.208x + 314.019418 + x2 = 0 + 314.019418

Reorder the terms:
-314.019418 + 314.019418 + -24673.208x + x2 = 0 + 314.019418

Combine like terms: -314.019418 + 314.019418 = 0.000000
0.000000 + -24673.208x + x2 = 0 + 314.019418
-24673.208x + x2 = 0 + 314.019418

Combine like terms: 0 + 314.019418 = 314.019418
-24673.208x + x2 = 314.019418

The x term is -24673.208x.  Take half its coefficient (-12336.604).
Square it (152191798.3) and add it to both sides.

Add '152191798.3' to each side of the equation.
-24673.208x + 152191798.3 + x2 = 314.019418 + 152191798.3

Reorder the terms:
152191798.3 + -24673.208x + x2 = 314.019418 + 152191798.3

Combine like terms: 314.019418 + 152191798.3 = 152192112.319418
152191798.3 + -24673.208x + x2 = 152192112.319418

Factor a perfect square on the left side:
(x + -12336.604)(x + -12336.604) = 152192112.319418

Calculate the square root of the right side: 12336.616729048

Break this problem into two subproblems by setting 
(x + -12336.604) equal to 12336.616729048 and -12336.616729048.


Subproblem 1
x + -12336.604 = 12336.616729048

Simplifying
x + -12336.604 = 12336.616729048

Reorder the terms:
-12336.604 + x = 12336.616729048

Solving
-12336.604 + x = 12336.616729048

Solving for variable 'x'.

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

Add '12336.604' to each side of the equation.
-12336.604 + 12336.604 + x = 12336.616729048 + 12336.604

Combine like terms: -12336.604 + 12336.604 = 0.000
0.000 + x = 12336.616729048 + 12336.604
x = 12336.616729048 + 12336.604

Combine like terms: 12336.616729048 + 12336.604 = 24673.220729048
x = 24673.220729048

Simplifying
x = 24673.220729048


Subproblem 2
x + -12336.604 = -12336.616729048

Simplifying
x + -12336.604 = -12336.616729048

Reorder the terms:
-12336.604 + x = -12336.616729048

Solving
-12336.604 + x = -12336.616729048

Solving for variable 'x'.

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

Add '12336.604' to each side of the equation.
-12336.604 + 12336.604 + x = -12336.616729048 + 12336.604

Combine like terms: -12336.604 + 12336.604 = 0.000
0.000 + x = -12336.616729048 + 12336.604
x = -12336.616729048 + 12336.604

Combine like terms: -12336.616729048 + 12336.604 = -0.012729048
x = -0.012729048

Simplifying
x = -0.012729048


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {24673.220729048, -0.012729048}

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