x^2-600x+90=0

Solution for x^2-600x+90=0 equation:

Simplifying
x2 + -600x + 90 = 0

Reorder the terms:
90 + -600x + x2 = 0

Solving
90 + -600x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-90' to each side of the equation.
90 + -600x + -90 + x2 = 0 + -90

Reorder the terms:
90 + -90 + -600x + x2 = 0 + -90

Combine like terms: 90 + -90 = 0
0 + -600x + x2 = 0 + -90
-600x + x2 = 0 + -90

Combine like terms: 0 + -90 = -90
-600x + x2 = -90

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 = -90 + 90000

Reorder the terms:
90000 + -600x + x2 = -90 + 90000

Combine like terms: -90 + 90000 = 89910
90000 + -600x + x2 = 89910

Factor a perfect square on the left side:
(x + -300)(x + -300) = 89910

Calculate the square root of the right side: 299.849962481

Break this problem into two subproblems by setting 
(x + -300) equal to 299.849962481 and -299.849962481.

Subproblem 1
x + -300 = 299.849962481

Simplifying
x + -300 = 299.849962481

Reorder the terms:
-300 + x = 299.849962481

Solving
-300 + x = 299.849962481

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 = 299.849962481 + 300

Combine like terms: -300 + 300 = 0
0 + x = 299.849962481 + 300
x = 299.849962481 + 300

Combine like terms: 299.849962481 + 300 = 599.849962481
x = 599.849962481

Simplifying
x = 599.849962481

Subproblem 2
x + -300 = -299.849962481

Simplifying
x + -300 = -299.849962481

Reorder the terms:
-300 + x = -299.849962481

Solving
-300 + x = -299.849962481

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 = -299.849962481 + 300

Combine like terms: -300 + 300 = 0
0 + x = -299.849962481 + 300
x = -299.849962481 + 300

Combine like terms: -299.849962481 + 300 = 0.150037519
x = 0.150037519

Simplifying
x = 0.150037519

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {599.849962481, 0.150037519}