x^2-500*x+1000=0

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Solution for x^2-500*x+1000=0 equation:


Simplifying
x2 + -500x + 1000 = 0

Reorder the terms:
1000 + -500x + x2 = 0

Solving
1000 + -500x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-1000' to each side of the equation.
1000 + -500x + -1000 + x2 = 0 + -1000

Reorder the terms:
1000 + -1000 + -500x + x2 = 0 + -1000

Combine like terms: 1000 + -1000 = 0
0 + -500x + x2 = 0 + -1000
-500x + x2 = 0 + -1000

Combine like terms: 0 + -1000 = -1000
-500x + x2 = -1000

The x term is -500x.  Take half its coefficient (-250).
Square it (62500) and add it to both sides.

Add '62500' to each side of the equation.
-500x + 62500 + x2 = -1000 + 62500

Reorder the terms:
62500 + -500x + x2 = -1000 + 62500

Combine like terms: -1000 + 62500 = 61500
62500 + -500x + x2 = 61500

Factor a perfect square on the left side:
(x + -250)(x + -250) = 61500

Calculate the square root of the right side: 247.991935353

Break this problem into two subproblems by setting 
(x + -250) equal to 247.991935353 and -247.991935353.

Subproblem 1

x + -250 = 247.991935353 Simplifying x + -250 = 247.991935353 Reorder the terms: -250 + x = 247.991935353 Solving -250 + x = 247.991935353 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '250' to each side of the equation. -250 + 250 + x = 247.991935353 + 250 Combine like terms: -250 + 250 = 0 0 + x = 247.991935353 + 250 x = 247.991935353 + 250 Combine like terms: 247.991935353 + 250 = 497.991935353 x = 497.991935353 Simplifying x = 497.991935353

Subproblem 2

x + -250 = -247.991935353 Simplifying x + -250 = -247.991935353 Reorder the terms: -250 + x = -247.991935353 Solving -250 + x = -247.991935353 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '250' to each side of the equation. -250 + 250 + x = -247.991935353 + 250 Combine like terms: -250 + 250 = 0 0 + x = -247.991935353 + 250 x = -247.991935353 + 250 Combine like terms: -247.991935353 + 250 = 2.008064647 x = 2.008064647 Simplifying x = 2.008064647

Solution

The solution to the problem is based on the solutions from the subproblems. x = {497.991935353, 2.008064647}

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