x^2-490x+2000=0

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Solution for x^2-490x+2000=0 equation: 


Simplifying
x2 + -490x + 2000 = 0

Reorder the terms:
2000 + -490x + x2 = 0

Solving
2000 + -490x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2000' to each side of the equation.
2000 + -490x + -2000 + x2 = 0 + -2000

Reorder the terms:
2000 + -2000 + -490x + x2 = 0 + -2000

Combine like terms: 2000 + -2000 = 0
0 + -490x + x2 = 0 + -2000
-490x + x2 = 0 + -2000

Combine like terms: 0 + -2000 = -2000
-490x + x2 = -2000

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 = -2000 + 60025

Reorder the terms:
60025 + -490x + x2 = -2000 + 60025

Combine like terms: -2000 + 60025 = 58025
60025 + -490x + x2 = 58025

Factor a perfect square on the left side:
(x + -245)(x + -245) = 58025

Calculate the square root of the right side: 240.883789409

Break this problem into two subproblems by setting 
(x + -245) equal to 240.883789409 and -240.883789409.


Subproblem 1
x + -245 = 240.883789409

Simplifying
x + -245 = 240.883789409

Reorder the terms:
-245 + x = 240.883789409

Solving
-245 + x = 240.883789409

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 = 240.883789409 + 245

Combine like terms: -245 + 245 = 0
0 + x = 240.883789409 + 245
x = 240.883789409 + 245

Combine like terms: 240.883789409 + 245 = 485.883789409
x = 485.883789409

Simplifying
x = 485.883789409


Subproblem 2
x + -245 = -240.883789409

Simplifying
x + -245 = -240.883789409

Reorder the terms:
-245 + x = -240.883789409

Solving
-245 + x = -240.883789409

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 = -240.883789409 + 245

Combine like terms: -245 + 245 = 0
0 + x = -240.883789409 + 245
x = -240.883789409 + 245

Combine like terms: -240.883789409 + 245 = 4.116210591
x = 4.116210591

Simplifying
x = 4.116210591


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {485.883789409, 4.116210591}

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