x^2+600x+20000=0

Solution for x^2+600x+20000=0 equation:

Simplifying
x2 + 600x + 20000 = 0

Reorder the terms:
20000 + 600x + x2 = 0

Solving
20000 + 600x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-20000' to each side of the equation.
20000 + 600x + -20000 + x2 = 0 + -20000

Reorder the terms:
20000 + -20000 + 600x + x2 = 0 + -20000

Combine like terms: 20000 + -20000 = 0
0 + 600x + x2 = 0 + -20000
600x + x2 = 0 + -20000

Combine like terms: 0 + -20000 = -20000
600x + x2 = -20000

The x term is 600x.  Take half its coefficient (300).
Square it (90000) and add it to both sides.

Add '90000' to each side of the equation.
600x + 90000 + x2 = -20000 + 90000

Reorder the terms:
90000 + 600x + x2 = -20000 + 90000

Combine like terms: -20000 + 90000 = 70000
90000 + 600x + x2 = 70000

Factor a perfect square on the left side:
(x + 300)(x + 300) = 70000

Calculate the square root of the right side: 264.575131106

Break this problem into two subproblems by setting 
(x + 300) equal to 264.575131106 and -264.575131106.

Subproblem 1
x + 300 = 264.575131106

Simplifying
x + 300 = 264.575131106

Reorder the terms:
300 + x = 264.575131106

Solving
300 + x = 264.575131106

Solving for variable 'x'.

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

Add '-300' to each side of the equation.
300 + -300 + x = 264.575131106 + -300

Combine like terms: 300 + -300 = 0
0 + x = 264.575131106 + -300
x = 264.575131106 + -300

Combine like terms: 264.575131106 + -300 = -35.424868894
x = -35.424868894

Simplifying
x = -35.424868894

Subproblem 2
x + 300 = -264.575131106

Simplifying
x + 300 = -264.575131106

Reorder the terms:
300 + x = -264.575131106

Solving
300 + x = -264.575131106

Solving for variable 'x'.

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

Add '-300' to each side of the equation.
300 + -300 + x = -264.575131106 + -300

Combine like terms: 300 + -300 = 0
0 + x = -264.575131106 + -300
x = -264.575131106 + -300

Combine like terms: -264.575131106 + -300 = -564.575131106
x = -564.575131106

Simplifying
x = -564.575131106

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-35.424868894, -564.575131106}