x^2-500x+4000=0

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Solution for x^2-500x+4000=0 equation:


Simplifying
x2 + -500x + 4000 = 0

Reorder the terms:
4000 + -500x + x2 = 0

Solving
4000 + -500x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-4000' to each side of the equation.
4000 + -500x + -4000 + x2 = 0 + -4000

Reorder the terms:
4000 + -4000 + -500x + x2 = 0 + -4000

Combine like terms: 4000 + -4000 = 0
0 + -500x + x2 = 0 + -4000
-500x + x2 = 0 + -4000

Combine like terms: 0 + -4000 = -4000
-500x + x2 = -4000

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 = -4000 + 62500

Reorder the terms:
62500 + -500x + x2 = -4000 + 62500

Combine like terms: -4000 + 62500 = 58500
62500 + -500x + x2 = 58500

Factor a perfect square on the left side:
(x + -250)(x + -250) = 58500

Calculate the square root of the right side: 241.867732449

Break this problem into two subproblems by setting 
(x + -250) equal to 241.867732449 and -241.867732449.

Subproblem 1

x + -250 = 241.867732449 Simplifying x + -250 = 241.867732449 Reorder the terms: -250 + x = 241.867732449 Solving -250 + x = 241.867732449 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 = 241.867732449 + 250 Combine like terms: -250 + 250 = 0 0 + x = 241.867732449 + 250 x = 241.867732449 + 250 Combine like terms: 241.867732449 + 250 = 491.867732449 x = 491.867732449 Simplifying x = 491.867732449

Subproblem 2

x + -250 = -241.867732449 Simplifying x + -250 = -241.867732449 Reorder the terms: -250 + x = -241.867732449 Solving -250 + x = -241.867732449 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 = -241.867732449 + 250 Combine like terms: -250 + 250 = 0 0 + x = -241.867732449 + 250 x = -241.867732449 + 250 Combine like terms: -241.867732449 + 250 = 8.132267551 x = 8.132267551 Simplifying x = 8.132267551

Solution

The solution to the problem is based on the solutions from the subproblems. x = {491.867732449, 8.132267551}

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