x^2-490x+5000=0

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Solution for x^2-490x+5000=0 equation: 


Simplifying
x2 + -490x + 5000 = 0

Reorder the terms:
5000 + -490x + x2 = 0

Solving
5000 + -490x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-5000' to each side of the equation.
5000 + -490x + -5000 + x2 = 0 + -5000

Reorder the terms:
5000 + -5000 + -490x + x2 = 0 + -5000

Combine like terms: 5000 + -5000 = 0
0 + -490x + x2 = 0 + -5000
-490x + x2 = 0 + -5000

Combine like terms: 0 + -5000 = -5000
-490x + x2 = -5000

The x term is -490x.  Take half its coefficient (-245).
Square it (60025) and add it to both sides.

Add '60025' to each side of the equation.
-490x + 60025 + x2 = -5000 + 60025

Reorder the terms:
60025 + -490x + x2 = -5000 + 60025

Combine like terms: -5000 + 60025 = 55025
60025 + -490x + x2 = 55025

Factor a perfect square on the left side:
(x + -245)(x + -245) = 55025

Calculate the square root of the right side: 234.574082115

Break this problem into two subproblems by setting 
(x + -245) equal to 234.574082115 and -234.574082115.


Subproblem 1
x + -245 = 234.574082115

Simplifying
x + -245 = 234.574082115

Reorder the terms:
-245 + x = 234.574082115

Solving
-245 + x = 234.574082115

Solving for variable 'x'.

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

Add '245' to each side of the equation.
-245 + 245 + x = 234.574082115 + 245

Combine like terms: -245 + 245 = 0
0 + x = 234.574082115 + 245
x = 234.574082115 + 245

Combine like terms: 234.574082115 + 245 = 479.574082115
x = 479.574082115

Simplifying
x = 479.574082115


Subproblem 2
x + -245 = -234.574082115

Simplifying
x + -245 = -234.574082115

Reorder the terms:
-245 + x = -234.574082115

Solving
-245 + x = -234.574082115

Solving for variable 'x'.

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

Add '245' to each side of the equation.
-245 + 245 + x = -234.574082115 + 245

Combine like terms: -245 + 245 = 0
0 + x = -234.574082115 + 245
x = -234.574082115 + 245

Combine like terms: -234.574082115 + 245 = 10.425917885
x = 10.425917885

Simplifying
x = 10.425917885


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {479.574082115, 10.425917885}

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