x^2-100x-600=0

Solution for x^2-100x-600=0 equation:

Simplifying
x2 + -100x + -600 = 0

Reorder the terms:
-600 + -100x + x2 = 0

Solving
-600 + -100x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '600' to each side of the equation.
-600 + -100x + 600 + x2 = 0 + 600

Reorder the terms:
-600 + 600 + -100x + x2 = 0 + 600

Combine like terms: -600 + 600 = 0
0 + -100x + x2 = 0 + 600
-100x + x2 = 0 + 600

Combine like terms: 0 + 600 = 600
-100x + x2 = 600

The x term is -100x.  Take half its coefficient (-50).
Square it (2500) and add it to both sides.

Add '2500' to each side of the equation.
-100x + 2500 + x2 = 600 + 2500

Reorder the terms:
2500 + -100x + x2 = 600 + 2500

Combine like terms: 600 + 2500 = 3100
2500 + -100x + x2 = 3100

Factor a perfect square on the left side:
(x + -50)(x + -50) = 3100

Calculate the square root of the right side: 55.677643628

Break this problem into two subproblems by setting 
(x + -50) equal to 55.677643628 and -55.677643628.

Subproblem 1
x + -50 = 55.677643628

Simplifying
x + -50 = 55.677643628

Reorder the terms:
-50 + x = 55.677643628

Solving
-50 + x = 55.677643628

Solving for variable 'x'.

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

Add '50' to each side of the equation.
-50 + 50 + x = 55.677643628 + 50

Combine like terms: -50 + 50 = 0
0 + x = 55.677643628 + 50
x = 55.677643628 + 50

Combine like terms: 55.677643628 + 50 = 105.677643628
x = 105.677643628

Simplifying
x = 105.677643628

Subproblem 2
x + -50 = -55.677643628

Simplifying
x + -50 = -55.677643628

Reorder the terms:
-50 + x = -55.677643628

Solving
-50 + x = -55.677643628

Solving for variable 'x'.

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

Add '50' to each side of the equation.
-50 + 50 + x = -55.677643628 + 50

Combine like terms: -50 + 50 = 0
0 + x = -55.677643628 + 50
x = -55.677643628 + 50

Combine like terms: -55.677643628 + 50 = -5.677643628
x = -5.677643628

Simplifying
x = -5.677643628

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {105.677643628, -5.677643628}