x^2+200x-105000=0

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Solution for x^2+200x-105000=0 equation: 


Simplifying
x2 + 200x + -105000 = 0

Reorder the terms:
-105000 + 200x + x2 = 0

Solving
-105000 + 200x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '105000' to each side of the equation.
-105000 + 200x + 105000 + x2 = 0 + 105000

Reorder the terms:
-105000 + 105000 + 200x + x2 = 0 + 105000

Combine like terms: -105000 + 105000 = 0
0 + 200x + x2 = 0 + 105000
200x + x2 = 0 + 105000

Combine like terms: 0 + 105000 = 105000
200x + x2 = 105000

The x term is 200x.  Take half its coefficient (100).
Square it (10000) and add it to both sides.

Add '10000' to each side of the equation.
200x + 10000 + x2 = 105000 + 10000

Reorder the terms:
10000 + 200x + x2 = 105000 + 10000

Combine like terms: 105000 + 10000 = 115000
10000 + 200x + x2 = 115000

Factor a perfect square on the left side:
(x + 100)(x + 100) = 115000

Calculate the square root of the right side: 339.116499156

Break this problem into two subproblems by setting 
(x + 100) equal to 339.116499156 and -339.116499156.


Subproblem 1
x + 100 = 339.116499156

Simplifying
x + 100 = 339.116499156

Reorder the terms:
100 + x = 339.116499156

Solving
100 + x = 339.116499156

Solving for variable 'x'.

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

Add '-100' to each side of the equation.
100 + -100 + x = 339.116499156 + -100

Combine like terms: 100 + -100 = 0
0 + x = 339.116499156 + -100
x = 339.116499156 + -100

Combine like terms: 339.116499156 + -100 = 239.116499156
x = 239.116499156

Simplifying
x = 239.116499156


Subproblem 2
x + 100 = -339.116499156

Simplifying
x + 100 = -339.116499156

Reorder the terms:
100 + x = -339.116499156

Solving
100 + x = -339.116499156

Solving for variable 'x'.

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

Add '-100' to each side of the equation.
100 + -100 + x = -339.116499156 + -100

Combine like terms: 100 + -100 = 0
0 + x = -339.116499156 + -100
x = -339.116499156 + -100

Combine like terms: -339.116499156 + -100 = -439.116499156
x = -439.116499156

Simplifying
x = -439.116499156


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {239.116499156, -439.116499156}

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