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.

Move the constant term to the right:

Add '-314.019418' to each side of the equation.
314.019418 + 24673.20799626468x + -314.019418 + x2 = 0 + -314.019418

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

Combine like terms: 314.019418 + -314.019418 = 0.000000
0.000000 + 24673.20799626468x + x2 = 0 + -314.019418
24673.20799626468x + x2 = 0 + -314.019418

Combine like terms: 0 + -314.019418 = -314.019418
24673.20799626468x + x2 = -314.019418

The x term is 24673.20799626468x.  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.
24673.20799626468x + 152191798.3 + x2 = -314.019418 + 152191798.3

Reorder the terms:
152191798.3 + 24673.20799626468x + x2 = -314.019418 + 152191798.3

Combine like terms: -314.019418 + 152191798.3 = 152191484.280582
152191798.3 + 24673.20799626468x + x2 = 152191484.280582

Factor a perfect square on the left side:
(x + 12336.604)(x + 12336.604) = 152191484.280582

Calculate the square root of the right side: 12336.591274764

Break this problem into two subproblems by setting 
(x + 12336.604) equal to 12336.591274764 and -12336.591274764.


Subproblem 1
x + 12336.604 = 12336.591274764

Simplifying
x + 12336.604 = 12336.591274764

Reorder the terms:
12336.604 + x = 12336.591274764

Solving
12336.604 + x = 12336.591274764

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 = 12336.591274764 + -12336.604

Combine like terms: 12336.604 + -12336.604 = 0.000
0.000 + x = 12336.591274764 + -12336.604
x = 12336.591274764 + -12336.604

Combine like terms: 12336.591274764 + -12336.604 = -0.012725236
x = -0.012725236

Simplifying
x = -0.012725236


Subproblem 2
x + 12336.604 = -12336.591274764

Simplifying
x + 12336.604 = -12336.591274764

Reorder the terms:
12336.604 + x = -12336.591274764

Solving
12336.604 + x = -12336.591274764

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 = -12336.591274764 + -12336.604

Combine like terms: 12336.604 + -12336.604 = 0.000
0.000 + x = -12336.591274764 + -12336.604
x = -12336.591274764 + -12336.604

Combine like terms: -12336.591274764 + -12336.604 = -24673.195274764
x = -24673.195274764

Simplifying
x = -24673.195274764


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.012725236, -24673.195274764}

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