x^2-400x+6000=0

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Solution for x^2-400x+6000=0 equation: 


Simplifying
x2 + -400x + 6000 = 0

Reorder the terms:
6000 + -400x + x2 = 0

Solving
6000 + -400x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-6000' to each side of the equation.
6000 + -400x + -6000 + x2 = 0 + -6000

Reorder the terms:
6000 + -6000 + -400x + x2 = 0 + -6000

Combine like terms: 6000 + -6000 = 0
0 + -400x + x2 = 0 + -6000
-400x + x2 = 0 + -6000

Combine like terms: 0 + -6000 = -6000
-400x + x2 = -6000

The x term is -400x.  Take half its coefficient (-200).
Square it (40000) and add it to both sides.

Add '40000' to each side of the equation.
-400x + 40000 + x2 = -6000 + 40000

Reorder the terms:
40000 + -400x + x2 = -6000 + 40000

Combine like terms: -6000 + 40000 = 34000
40000 + -400x + x2 = 34000

Factor a perfect square on the left side:
(x + -200)(x + -200) = 34000

Calculate the square root of the right side: 184.390889146

Break this problem into two subproblems by setting 
(x + -200) equal to 184.390889146 and -184.390889146.


Subproblem 1
x + -200 = 184.390889146

Simplifying
x + -200 = 184.390889146

Reorder the terms:
-200 + x = 184.390889146

Solving
-200 + x = 184.390889146

Solving for variable 'x'.

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

Add '200' to each side of the equation.
-200 + 200 + x = 184.390889146 + 200

Combine like terms: -200 + 200 = 0
0 + x = 184.390889146 + 200
x = 184.390889146 + 200

Combine like terms: 184.390889146 + 200 = 384.390889146
x = 384.390889146

Simplifying
x = 384.390889146


Subproblem 2
x + -200 = -184.390889146

Simplifying
x + -200 = -184.390889146

Reorder the terms:
-200 + x = -184.390889146

Solving
-200 + x = -184.390889146

Solving for variable 'x'.

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

Add '200' to each side of the equation.
-200 + 200 + x = -184.390889146 + 200

Combine like terms: -200 + 200 = 0
0 + x = -184.390889146 + 200
x = -184.390889146 + 200

Combine like terms: -184.390889146 + 200 = 15.609110854
x = 15.609110854

Simplifying
x = 15.609110854


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {384.390889146, 15.609110854}

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