x^2-860x-2500=0

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Solution for x^2-860x-2500=0 equation: 


Simplifying
x2 + -860x + -2500 = 0

Reorder the terms:
-2500 + -860x + x2 = 0

Solving
-2500 + -860x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '2500' to each side of the equation.
-2500 + -860x + 2500 + x2 = 0 + 2500

Reorder the terms:
-2500 + 2500 + -860x + x2 = 0 + 2500

Combine like terms: -2500 + 2500 = 0
0 + -860x + x2 = 0 + 2500
-860x + x2 = 0 + 2500

Combine like terms: 0 + 2500 = 2500
-860x + x2 = 2500

The x term is -860x.  Take half its coefficient (-430).
Square it (184900) and add it to both sides.

Add '184900' to each side of the equation.
-860x + 184900 + x2 = 2500 + 184900

Reorder the terms:
184900 + -860x + x2 = 2500 + 184900

Combine like terms: 2500 + 184900 = 187400
184900 + -860x + x2 = 187400

Factor a perfect square on the left side:
(x + -430)(x + -430) = 187400

Calculate the square root of the right side: 432.897216438

Break this problem into two subproblems by setting 
(x + -430) equal to 432.897216438 and -432.897216438.


Subproblem 1
x + -430 = 432.897216438

Simplifying
x + -430 = 432.897216438

Reorder the terms:
-430 + x = 432.897216438

Solving
-430 + x = 432.897216438

Solving for variable 'x'.

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

Add '430' to each side of the equation.
-430 + 430 + x = 432.897216438 + 430

Combine like terms: -430 + 430 = 0
0 + x = 432.897216438 + 430
x = 432.897216438 + 430

Combine like terms: 432.897216438 + 430 = 862.897216438
x = 862.897216438

Simplifying
x = 862.897216438


Subproblem 2
x + -430 = -432.897216438

Simplifying
x + -430 = -432.897216438

Reorder the terms:
-430 + x = -432.897216438

Solving
-430 + x = -432.897216438

Solving for variable 'x'.

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

Add '430' to each side of the equation.
-430 + 430 + x = -432.897216438 + 430

Combine like terms: -430 + 430 = 0
0 + x = -432.897216438 + 430
x = -432.897216438 + 430

Combine like terms: -432.897216438 + 430 = -2.897216438
x = -2.897216438

Simplifying
x = -2.897216438


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {862.897216438, -2.897216438}

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