x^2-3000x+1600=0

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Solution for x^2-3000x+1600=0 equation: 


Simplifying
x2 + -3000x + 1600 = 0

Reorder the terms:
1600 + -3000x + x2 = 0

Solving
1600 + -3000x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-1600' to each side of the equation.
1600 + -3000x + -1600 + x2 = 0 + -1600

Reorder the terms:
1600 + -1600 + -3000x + x2 = 0 + -1600

Combine like terms: 1600 + -1600 = 0
0 + -3000x + x2 = 0 + -1600
-3000x + x2 = 0 + -1600

Combine like terms: 0 + -1600 = -1600
-3000x + x2 = -1600

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 = -1600 + 2250000

Reorder the terms:
2250000 + -3000x + x2 = -1600 + 2250000

Combine like terms: -1600 + 2250000 = 2248400
2250000 + -3000x + x2 = 2248400

Factor a perfect square on the left side:
(x + -1500)(x + -1500) = 2248400

Calculate the square root of the right side: 1499.466571818

Break this problem into two subproblems by setting 
(x + -1500) equal to 1499.466571818 and -1499.466571818.


Subproblem 1
x + -1500 = 1499.466571818

Simplifying
x + -1500 = 1499.466571818

Reorder the terms:
-1500 + x = 1499.466571818

Solving
-1500 + x = 1499.466571818

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 = 1499.466571818 + 1500

Combine like terms: -1500 + 1500 = 0
0 + x = 1499.466571818 + 1500
x = 1499.466571818 + 1500

Combine like terms: 1499.466571818 + 1500 = 2999.466571818
x = 2999.466571818

Simplifying
x = 2999.466571818


Subproblem 2
x + -1500 = -1499.466571818

Simplifying
x + -1500 = -1499.466571818

Reorder the terms:
-1500 + x = -1499.466571818

Solving
-1500 + x = -1499.466571818

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 = -1499.466571818 + 1500

Combine like terms: -1500 + 1500 = 0
0 + x = -1499.466571818 + 1500
x = -1499.466571818 + 1500

Combine like terms: -1499.466571818 + 1500 = 0.533428182
x = 0.533428182

Simplifying
x = 0.533428182


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2999.466571818, 0.533428182}

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