X^2+2500X-351792=0

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Solution for X^2+2500X-351792=0 equation: 


Simplifying
X2 + 2500X + -351792 = 0

Reorder the terms:
-351792 + 2500X + X2 = 0

Solving
-351792 + 2500X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '351792' to each side of the equation.
-351792 + 2500X + 351792 + X2 = 0 + 351792

Reorder the terms:
-351792 + 351792 + 2500X + X2 = 0 + 351792

Combine like terms: -351792 + 351792 = 0
0 + 2500X + X2 = 0 + 351792
2500X + X2 = 0 + 351792

Combine like terms: 0 + 351792 = 351792
2500X + X2 = 351792

The X term is 2500X.  Take half its coefficient (1250).
Square it (1562500) and add it to both sides.

Add '1562500' to each side of the equation.
2500X + 1562500 + X2 = 351792 + 1562500

Reorder the terms:
1562500 + 2500X + X2 = 351792 + 1562500

Combine like terms: 351792 + 1562500 = 1914292
1562500 + 2500X + X2 = 1914292

Factor a perfect square on the left side:
(X + 1250)(X + 1250) = 1914292

Calculate the square root of the right side: 1383.579415863

Break this problem into two subproblems by setting 
(X + 1250) equal to 1383.579415863 and -1383.579415863.


Subproblem 1
X + 1250 = 1383.579415863

Simplifying
X + 1250 = 1383.579415863

Reorder the terms:
1250 + X = 1383.579415863

Solving
1250 + X = 1383.579415863

Solving for variable 'X'.

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

Add '-1250' to each side of the equation.
1250 + -1250 + X = 1383.579415863 + -1250

Combine like terms: 1250 + -1250 = 0
0 + X = 1383.579415863 + -1250
X = 1383.579415863 + -1250

Combine like terms: 1383.579415863 + -1250 = 133.579415863
X = 133.579415863

Simplifying
X = 133.579415863


Subproblem 2
X + 1250 = -1383.579415863

Simplifying
X + 1250 = -1383.579415863

Reorder the terms:
1250 + X = -1383.579415863

Solving
1250 + X = -1383.579415863

Solving for variable 'X'.

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

Add '-1250' to each side of the equation.
1250 + -1250 + X = -1383.579415863 + -1250

Combine like terms: 1250 + -1250 = 0
0 + X = -1383.579415863 + -1250
X = -1383.579415863 + -1250

Combine like terms: -1383.579415863 + -1250 = -2633.579415863
X = -2633.579415863

Simplifying
X = -2633.579415863


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {133.579415863, -2633.579415863}

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