x^2-3000x+300000=0

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Solution for x^2-3000x+300000=0 equation: 


Simplifying
x2 + -3000x + 300000 = 0

Reorder the terms:
300000 + -3000x + x2 = 0

Solving
300000 + -3000x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-300000' to each side of the equation.
300000 + -3000x + -300000 + x2 = 0 + -300000

Reorder the terms:
300000 + -300000 + -3000x + x2 = 0 + -300000

Combine like terms: 300000 + -300000 = 0
0 + -3000x + x2 = 0 + -300000
-3000x + x2 = 0 + -300000

Combine like terms: 0 + -300000 = -300000
-3000x + x2 = -300000

The x term is -3000x.  Take half its coefficient (-1500).
Square it (2250000) and add it to both sides.

Add '2250000' to each side of the equation.
-3000x + 2250000 + x2 = -300000 + 2250000

Reorder the terms:
2250000 + -3000x + x2 = -300000 + 2250000

Combine like terms: -300000 + 2250000 = 1950000
2250000 + -3000x + x2 = 1950000

Factor a perfect square on the left side:
(x + -1500)(x + -1500) = 1950000

Calculate the square root of the right side: 1396.424004377

Break this problem into two subproblems by setting 
(x + -1500) equal to 1396.424004377 and -1396.424004377.


Subproblem 1
x + -1500 = 1396.424004377

Simplifying
x + -1500 = 1396.424004377

Reorder the terms:
-1500 + x = 1396.424004377

Solving
-1500 + x = 1396.424004377

Solving for variable 'x'.

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

Add '1500' to each side of the equation.
-1500 + 1500 + x = 1396.424004377 + 1500

Combine like terms: -1500 + 1500 = 0
0 + x = 1396.424004377 + 1500
x = 1396.424004377 + 1500

Combine like terms: 1396.424004377 + 1500 = 2896.424004377
x = 2896.424004377

Simplifying
x = 2896.424004377


Subproblem 2
x + -1500 = -1396.424004377

Simplifying
x + -1500 = -1396.424004377

Reorder the terms:
-1500 + x = -1396.424004377

Solving
-1500 + x = -1396.424004377

Solving for variable 'x'.

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

Add '1500' to each side of the equation.
-1500 + 1500 + x = -1396.424004377 + 1500

Combine like terms: -1500 + 1500 = 0
0 + x = -1396.424004377 + 1500
x = -1396.424004377 + 1500

Combine like terms: -1396.424004377 + 1500 = 103.575995623
x = 103.575995623

Simplifying
x = 103.575995623


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2896.424004377, 103.575995623}

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