200x^2-9200x-98838=0

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Solution for 200x^2-9200x-98838=0 equation: 


Simplifying
200x2 + -9200x + -98838 = 0

Reorder the terms:
-98838 + -9200x + 200x2 = 0

Solving
-98838 + -9200x + 200x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-49419 + -4600x + 100x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-49419 + -4600x + 100x2)' equal to zero and attempt to solve:

Simplifying
-49419 + -4600x + 100x2 = 0

Solving
-49419 + -4600x + 100x2 = 0

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

Divide each side by '100'.
-494.19 + -46x + x2 = 0.00

Move the constant term to the right:

Add '494.19' to each side of the equation.
-494.19 + -46x + 494.19 + x2 = 0.00 + 494.19

Reorder the terms:
-494.19 + 494.19 + -46x + x2 = 0.00 + 494.19

Combine like terms: -494.19 + 494.19 = 0.00
0.00 + -46x + x2 = 0.00 + 494.19
-46x + x2 = 0.00 + 494.19

Combine like terms: 0.00 + 494.19 = 494.19
-46x + x2 = 494.19

The x term is -46x.  Take half its coefficient (-23).
Square it (529) and add it to both sides.

Add '529' to each side of the equation.
-46x + 529 + x2 = 494.19 + 529

Reorder the terms:
529 + -46x + x2 = 494.19 + 529

Combine like terms: 494.19 + 529 = 1023.19
529 + -46x + x2 = 1023.19

Factor a perfect square on the left side:
(x + -23)(x + -23) = 1023.19

Calculate the square root of the right side: 31.987341246

Break this problem into two subproblems by setting 
(x + -23) equal to 31.987341246 and -31.987341246.


Subproblem 1
x + -23 = 31.987341246

Simplifying
x + -23 = 31.987341246

Reorder the terms:
-23 + x = 31.987341246

Solving
-23 + x = 31.987341246

Solving for variable 'x'.

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

Add '23' to each side of the equation.
-23 + 23 + x = 31.987341246 + 23

Combine like terms: -23 + 23 = 0
0 + x = 31.987341246 + 23
x = 31.987341246 + 23

Combine like terms: 31.987341246 + 23 = 54.987341246
x = 54.987341246

Simplifying
x = 54.987341246


Subproblem 2
x + -23 = -31.987341246

Simplifying
x + -23 = -31.987341246

Reorder the terms:
-23 + x = -31.987341246

Solving
-23 + x = -31.987341246

Solving for variable 'x'.

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

Add '23' to each side of the equation.
-23 + 23 + x = -31.987341246 + 23

Combine like terms: -23 + 23 = 0
0 + x = -31.987341246 + 23
x = -31.987341246 + 23

Combine like terms: -31.987341246 + 23 = -8.987341246
x = -8.987341246

Simplifying
x = -8.987341246


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {54.987341246, -8.987341246}
Solution
x = {54.987341246, -8.987341246}

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