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 = 1900
2500 + -100x + x2 = 1900

Factor a perfect square on the left side:
(x + -50)(x + -50) = 1900

Calculate the square root of the right side: 43.588989435

Break this problem into two subproblems by setting 
(x + -50) equal to 43.588989435 and -43.588989435.

Subproblem 1
x + -50 = 43.588989435

Simplifying
x + -50 = 43.588989435

Reorder the terms:
-50 + x = 43.588989435

Solving
-50 + x = 43.588989435

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 = 43.588989435 + 50

Combine like terms: -50 + 50 = 0
0 + x = 43.588989435 + 50
x = 43.588989435 + 50

Combine like terms: 43.588989435 + 50 = 93.588989435
x = 93.588989435

Simplifying
x = 93.588989435

Subproblem 2
x + -50 = -43.588989435

Simplifying
x + -50 = -43.588989435

Reorder the terms:
-50 + x = -43.588989435

Solving
-50 + x = -43.588989435

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 = -43.588989435 + 50

Combine like terms: -50 + 50 = 0
0 + x = -43.588989435 + 50
x = -43.588989435 + 50

Combine like terms: -43.588989435 + 50 = 6.411010565
x = 6.411010565

Simplifying
x = 6.411010565

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {93.588989435, 6.411010565}