x^2-1200x+335=0

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Solution for x^2-1200x+335=0 equation: 


Simplifying
x2 + -1200x + 335 = 0

Reorder the terms:
335 + -1200x + x2 = 0

Solving
335 + -1200x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-335' to each side of the equation.
335 + -1200x + -335 + x2 = 0 + -335

Reorder the terms:
335 + -335 + -1200x + x2 = 0 + -335

Combine like terms: 335 + -335 = 0
0 + -1200x + x2 = 0 + -335
-1200x + x2 = 0 + -335

Combine like terms: 0 + -335 = -335
-1200x + x2 = -335

The x term is -1200x.  Take half its coefficient (-600).
Square it (360000) and add it to both sides.

Add '360000' to each side of the equation.
-1200x + 360000 + x2 = -335 + 360000

Reorder the terms:
360000 + -1200x + x2 = -335 + 360000

Combine like terms: -335 + 360000 = 359665
360000 + -1200x + x2 = 359665

Factor a perfect square on the left side:
(x + -600)(x + -600) = 359665

Calculate the square root of the right side: 599.720768358

Break this problem into two subproblems by setting 
(x + -600) equal to 599.720768358 and -599.720768358.


Subproblem 1
x + -600 = 599.720768358

Simplifying
x + -600 = 599.720768358

Reorder the terms:
-600 + x = 599.720768358

Solving
-600 + x = 599.720768358

Solving for variable 'x'.

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

Add '600' to each side of the equation.
-600 + 600 + x = 599.720768358 + 600

Combine like terms: -600 + 600 = 0
0 + x = 599.720768358 + 600
x = 599.720768358 + 600

Combine like terms: 599.720768358 + 600 = 1199.720768358
x = 1199.720768358

Simplifying
x = 1199.720768358


Subproblem 2
x + -600 = -599.720768358

Simplifying
x + -600 = -599.720768358

Reorder the terms:
-600 + x = -599.720768358

Solving
-600 + x = -599.720768358

Solving for variable 'x'.

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

Add '600' to each side of the equation.
-600 + 600 + x = -599.720768358 + 600

Combine like terms: -600 + 600 = 0
0 + x = -599.720768358 + 600
x = -599.720768358 + 600

Combine like terms: -599.720768358 + 600 = 0.279231642
x = 0.279231642

Simplifying
x = 0.279231642


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1199.720768358, 0.279231642}

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